
#ifndef AFTERMATH_RANDOM_ZIGGURAT_NORMAL_HPP_INCLUDED
#define AFTERMATH_RANDOM_ZIGGURAT_NORMAL_HPP_INCLUDED

#include "ziggurat_core.hpp"

#include <cmath>
#include <cstdint>

namespace aftermath
{
    namespace random
    {
        template <std::uint_fast32_t t_n_boxes, typename t_uniform_type, typename t_bounds_type, t_bounds_type t_diameter>
        struct ziggurat_normal
            : public ziggurat_core<t_n_boxes, ziggurat_normal<t_n_boxes, t_uniform_type, t_bounds_type, t_diameter>, t_uniform_type, t_bounds_type, t_diameter, double>
        {
            static const std::uint_fast32_t n_boxes = t_n_boxes;
            static const t_bounds_type diameter = t_diameter;

            typedef t_uniform_type  uniform_type;
            typedef double          result_type;
            typedef t_bounds_type   bounds_type;
            typedef ziggurat_normal<n_boxes, uniform_type, bounds_type, diameter> type;
            typedef ziggurat_core<n_boxes, type, uniform_type, bounds_type, diameter, double> base_type;
            
            // Inherited typedef's:
            typedef type ziggurat_impl_type;

        private:
            const result_type  right_tail_x = 3.8520461503683912;
            const result_type  left_tail_x = -3.8520461503683912;
            const result_type  box_volume = 0.00098010797069741627;
            const uniform_type box_volume_diameter = static_cast<uniform_type>(box_volume * (type::diameter + 1));

            // Zero-based index of the box that covers the right tail.
            static const std::uint_fast32_t right_tail_index = 0;
            // Zero-based index of the box that covers the left tail.
            static const std::uint_fast32_t left_tail_index = n_boxes - 1;
            
            // (<diameter> + 1)-downscaled right (left) x-endpoints of the boxes, modified for the tail boxes: { x_0*, x_1, x_2, ..., x_{n - 1}, x_n* }.
            const result_type  m_width_scaled[n_boxes] = {
                4.0968586097934827 / (type::diameter + 1),      3.8520461503683912 / (type::diameter + 1),      3.6591529330911164 / (type::diameter + 1),      3.5387147915535359 / (type::diameter + 1),      3.4499415844581948 / (type::diameter + 1),      3.3791208509098653 / (type::diameter + 1),      3.3199242727525520 / (type::diameter + 1),      3.2688953201247243 / (type::diameter + 1),
                3.2239336074705574 / (type::diameter + 1),      3.1836646787008854 / (type::diameter + 1),      3.1471385926519712 / (type::diameter + 1),      3.1136706092218944 / (type::diameter + 1),      3.0827503897194092 / (type::diameter + 1),      3.0539870972903128 / (type::diameter + 1),      3.0270745842754689 / (type::diameter + 1),      3.0017684330687534 / (type::diameter + 1),
                2.9778703072041906 / (type::diameter + 1),      2.9552169815083583 / (type::diameter + 1),      2.9336724639032943 / (type::diameter + 1),      2.9131222169485817 / (type::diameter + 1),      2.8934688401496455 / (type::diameter + 1),      2.8746287902796272 / (type::diameter + 1),      2.8565298533366061 / (type::diameter + 1),      2.8391091700186590 / (type::diameter + 1),
                2.8223116750508611 / (type::diameter + 1),      2.8060888502170392 / (type::diameter + 1),      2.7903977181709911 / (type::diameter + 1),      2.7752000231739453 / (type::diameter + 1),      2.7604615584754485 / (type::diameter + 1),      2.7461516098484305 / (type::diameter + 1),      2.7322424919497175 / (type::diameter + 1),      2.7187091594759438 / (type::diameter + 1),
                2.7055288790496144 / (type::diameter + 1),      2.6926809507675676 / (type::diameter + 1),      2.6801464706321721 / (type::diameter + 1),      2.6679081268478898 / (type::diameter + 1),      2.6559500243346071 / (type::diameter + 1),      2.6442575328806557 / (type::diameter + 1),      2.6328171552034775 / (type::diameter + 1),      2.6216164118569691 / (type::diameter + 1),
                2.6106437404609705 / (type::diameter + 1),      2.5998884071598398 / (type::diameter + 1),      2.5893404285661339 / (type::diameter + 1),      2.5789905027294192 / (type::diameter + 1),      2.5688299479025083 / (type::diameter + 1),      2.5588506480683336 / (type::diameter + 1),      2.5490450043483498 / (type::diameter + 1),      2.5394058915441638 / (type::diameter + 1),
                2.5299266191730942 / (type::diameter + 1),      2.5206008964495547 / (type::diameter + 1),      2.5114228007407585 / (type::diameter + 1),      2.5023867490898326 / (type::diameter + 1),      2.4934874724540813 / (type::diameter + 1),      2.4847199923525551 / (type::diameter + 1),      2.4760795996566162 / (type::diameter + 1),      2.4675618352909908 / (type::diameter + 1),
                2.4591624726417722 / (type::diameter + 1),      2.4508775014927480 / (type::diameter + 1),      2.4427031133329121 / (type::diameter + 1),      2.4346356878965929 / (type::diameter + 1),      2.4266717808137350 / (type::diameter + 1),      2.4188081122618657 / (type::diameter + 1),      2.4110415565234738 / (type::diameter + 1),      2.4033691323631760 / (type::diameter + 1),
                2.3957879941483700 / (type::diameter + 1),      2.3882954236452498 / (type::diameter + 1),      2.3808888224292500 / (type::diameter + 1),      2.3735657048553191 / (type::diameter + 1),      2.3663236915390124 / (type::diameter + 1),      2.3591605033043417 / (type::diameter + 1),      2.3520739555587000 / (type::diameter + 1),      2.3450619530590706 / (type::diameter + 1),
                2.3381224850371873 / (type::diameter + 1),      2.3312536206543983 / (type::diameter + 1),      2.3244535047597318 / (type::diameter + 1),      2.3177203539271236 / (type::diameter + 1),      2.3110524527499645 / (type::diameter + 1),      2.3044481503730991 / (type::diameter + 1),      2.2979058572441794 / (type::diameter + 1),      2.2914240420678696 / (type::diameter + 1),
                2.2850012289478306 / (type::diameter + 1),      2.2786359947027097 / (type::diameter + 1),      2.2723269663435255 / (type::diameter + 1),      2.2660728187008963 / (type::diameter + 1),      2.2598722721915137 / (type::diameter + 1),      2.2537240907141323 / (type::diameter + 1),      2.2476270796661295 / (type::diameter + 1),      2.2415800840724064 / (type::diameter + 1),
                2.2355819868190481 / (type::diameter + 1),      2.2296317069847555 / (type::diameter + 1),      2.2237281982635985 / (type::diameter + 1),      2.2178704474731334 / (type::diameter + 1),      2.2120574731423764 / (type::diameter + 1),      2.2062883241745377 / (type::diameter + 1),      2.2005620785797949 / (type::diameter + 1),      2.1948778422737315 / (type::diameter + 1),
                2.1892347479373814 / (type::diameter + 1),      2.1836319539351109 / (type::diameter + 1),      2.1780686432868369 / (type::diameter + 1),      2.1725440226913261 / (type::diameter + 1),      2.1670573215975428 / (type::diameter + 1),      2.1616077913212271 / (type::diameter + 1),      2.1561947042040695 / (type::diameter + 1),      2.1508173528130321 / (type::diameter + 1),
                2.1454750491775266 / (type::diameter + 1),      2.1401671240623097 / (type::diameter + 1),      2.1348929262740997 / (type::diameter + 1),      2.1296518220000450 / (type::diameter + 1),      2.1244431941762954 / (type::diameter + 1),      2.1192664418850403 / (type::diameter + 1),      2.1141209797784779 / (type::diameter + 1),      2.1090062375282789 / (type::diameter + 1),
                2.1039216592991946 / (type::diameter + 1),      2.0988667032455423 / (type::diameter + 1),      2.0938408410293801 / (type::diameter + 1),      2.0888435573592524 / (type::diameter + 1),      2.0838743495484545 / (type::diameter + 1),      2.0789327270918298 / (type::diameter + 1),      2.0740182112601659 / (type::diameter + 1),      2.0691303347113164 / (type::diameter + 1),
                2.0642686411172195 / (type::diameter + 1),      2.0594326848060371 / (type::diameter + 1),      2.0546220304186797 / (type::diameter + 1),      2.0498362525790223 / (type::diameter + 1),      2.0450749355771602 / (type::diameter + 1),      2.0403376730650835 / (type::diameter + 1),      2.0356240677641887 / (type::diameter + 1),      2.0309337311840735 / (type::diameter + 1),
                2.0262662833520941 / (type::diameter + 1),      2.0216213525531890 / (type::diameter + 1),      2.0169985750795031 / (type::diameter + 1),      2.0123975949893673 / (type::diameter + 1),      2.0078180638752146 / (type::diameter + 1),      2.0032596406400350 / (type::diameter + 1),      1.9987219912819901 / (type::diameter + 1),      1.9942047886868308 / (type::diameter + 1),
                1.9897077124277773 / (type::diameter + 1),      1.9852304485725390 / (type::diameter + 1),      1.9807726894971676 / (type::diameter + 1),      1.9763341337064515 / (type::diameter + 1),      1.9719144856605762 / (type::diameter + 1),      1.9675134556077848 / (type::diameter + 1),      1.9631307594227913 / (type::diameter + 1),      1.9587661184507046 / (type::diameter + 1),
                1.9544192593562404 / (type::diameter + 1),      1.9500899139780004 / (type::diameter + 1),      1.9457778191876175 / (type::diameter + 1),      1.9414827167535663 / (type::diameter + 1),      1.9372043532094561 / (type::diameter + 1),      1.9329424797266246 / (type::diameter + 1),      1.9286968519908639 / (type::diameter + 1),      1.9244672300831170 / (type::diameter + 1),
                1.9202533783639877 / (type::diameter + 1),      1.9160550653619177 / (type::diameter + 1),      1.9118720636648895 / (type::diameter + 1),      1.9077041498155190 / (type::diameter + 1),      1.9035511042094096 / (type::diameter + 1),      1.8994127109966441 / (type::diameter + 1),      1.8952887579862965 / (type::diameter + 1),      1.8911790365538510 / (type::diameter + 1),
                1.8870833415514195 / (type::diameter + 1),      1.8830014712206555 / (type::diameter + 1),      1.8789332271082637 / (type::diameter + 1),      1.8748784139840128 / (type::diameter + 1),      1.8708368397611575 / (type::diameter + 1),      1.8668083154191869 / (type::diameter + 1),      1.8627926549288112 / (type::diameter + 1),      1.8587896751791113 / (type::diameter + 1),
                1.8547991959067708 / (type::diameter + 1),      1.8508210396273195 / (type::diameter + 1),      1.8468550315683164 / (type::diameter + 1),      1.8429009996044052 / (type::diameter + 1),      1.8389587741941765 / (type::diameter + 1),      1.8350281883187756 / (type::diameter + 1),      1.8311090774221942 / (type::diameter + 1),      1.8272012793531899 / (type::diameter + 1),
                1.8233046343087771 / (type::diameter + 1),      1.8194189847792369 / (type::diameter + 1),      1.8155441754945940 / (type::diameter + 1),      1.8116800533725120 / (type::diameter + 1),      1.8078264674675599 / (type::diameter + 1),      1.8039832689218035 / (type::diameter + 1),      1.8001503109166781 / (type::diameter + 1),      1.7963274486261016 / (type::diameter + 1),
                1.7925145391707853 / (type::diameter + 1),      1.7887114415737045 / (type::diameter + 1),      1.7849180167166913 / (type::diameter + 1),      1.7811341272981129 / (type::diameter + 1),      1.7773596377916004 / (type::diameter + 1),      1.7735944144057943 / (type::diameter + 1),      1.7698383250450752 / (type::diameter + 1),      1.7660912392712462 / (type::diameter + 1),
                1.7623530282661394 / (type::diameter + 1),      1.7586235647951147 / (type::diameter + 1),      1.7549027231714249 / (type::diameter + 1),      1.7511903792214188 / (type::diameter + 1),      1.7474864102505558 / (type::diameter + 1),      1.7437906950102073 / (type::diameter + 1),      1.7401031136652208 / (type::diameter + 1),      1.7364235477622212 / (type::diameter + 1),
                1.7327518801986285 / (type::diameter + 1),      1.7290879951923689 / (type::diameter + 1),      1.7254317782522580 / (type::diameter + 1),      1.7217831161490343 / (type::diameter + 1),      1.7181418968870262 / (type::diameter + 1),      1.7145080096764288 / (type::diameter + 1),      1.7108813449061757 / (type::diameter + 1),      1.7072617941173850 / (type::diameter + 1),
                1.7036492499773638 / (type::diameter + 1),      1.7000436062541523 / (type::diameter + 1),      1.6964447577915930 / (type::diameter + 1),      1.6928526004849079 / (type::diameter + 1),      1.6892670312567682 / (type::diameter + 1),      1.6856879480338421 / (type::diameter + 1),      1.6821152497238058 / (type::diameter + 1),      1.6785488361928036 / (type::diameter + 1),
                1.6749886082433434 / (type::diameter + 1),      1.6714344675926146 / (type::diameter + 1),      1.6678863168512151 / (type::diameter + 1),      1.6643440595022755 / (type::diameter + 1),      1.6608075998809673 / (type::diameter + 1),      1.6572768431543845 / (type::diameter + 1),      1.6537516953017864 / (type::diameter + 1),      1.6502320630951906 / (type::diameter + 1),
                1.6467178540803049 / (type::diameter + 1),      1.6432089765577891 / (type::diameter + 1),      1.6397053395648339 / (type::diameter + 1),      1.6362068528570498 / (type::diameter + 1),      1.6327134268906535 / (type::diameter + 1),      1.6292249728049442 / (type::diameter + 1),      1.6257414024050602 / (type::diameter + 1),      1.6222626281450062 / (type::diameter + 1),
                1.6187885631109426 / (type::diameter + 1),      1.6153191210047294 / (type::diameter + 1),      1.6118542161277145 / (type::diameter + 1),      1.6083937633647595 / (type::diameter + 1),      1.6049376781684953 / (type::diameter + 1),      1.6014858765437981 / (type::diameter + 1),      1.5980382750324798 / (type::diameter + 1),      1.5945947906981849 / (type::diameter + 1),
                1.5911553411114858 / (type::diameter + 1),      1.5877198443351710 / (type::diameter + 1),      1.5842882189097174 / (type::diameter + 1),      1.5808603838389411 / (type::diameter + 1),      1.5774362585758194 / (type::diameter + 1),      1.5740157630084784 / (type::diameter + 1),      1.5705988174463378 / (type::diameter + 1),      1.5671853426064083 / (type::diameter + 1),
                1.5637752595997354 / (type::diameter + 1),      1.5603684899179821 / (type::diameter + 1),      1.5569649554201453 / (type::diameter + 1),      1.5535645783194007 / (type::diameter + 1),      1.5501672811700688 / (type::diameter + 1),      1.5467729868546979 / (type::diameter + 1),      1.5433816185712570 / (type::diameter + 1),      1.5399930998204339 / (type::diameter + 1),
                1.5366073543930328 / (type::diameter + 1),      1.5332243063574660 / (type::diameter + 1),      1.5298438800473342 / (type::diameter + 1),      1.5264660000490895 / (type::diameter + 1),      1.5230905911897777 / (type::diameter + 1),      1.5197175785248521 / (type::diameter + 1),      1.5163468873260558 / (type::diameter + 1),      1.5129784430693663 / (type::diameter + 1),
                1.5096121714229974 / (type::diameter + 1),      1.5062479982354535 / (type::diameter + 1),      1.5028858495236314 / (type::diameter + 1),      1.4995256514609645 / (type::diameter + 1),      1.4961673303656038 / (type::diameter + 1),      1.4928108126886319 / (type::diameter + 1),      1.4894560250023045 / (type::diameter + 1),      1.4861028939883133 / (type::diameter + 1),
                1.4827513464260682 / (type::diameter + 1),      1.4794013091809903 / (type::diameter + 1),      1.4760527091928140 / (type::diameter + 1),      1.4727054734638911 / (type::diameter + 1),      1.4693595290474926 / (type::diameter + 1),      1.4660148030361038 / (type::diameter + 1),      1.4626712225497066 / (type::diameter + 1),      1.4593287147240453 / (type::diameter + 1),
                1.4559872066988694 / (type::diameter + 1),      1.4526466256061495 / (type::diameter + 1),      1.4493068985582607 / (type::diameter + 1),      1.4459679526361285 / (type::diameter + 1),      1.4426297148773315 / (type::diameter + 1),      1.4392921122641568 / (type::diameter + 1),      1.4359550717116014 / (type::diameter + 1),      1.4326185200553153 / (type::diameter + 1),
                1.4292823840394803 / (type::diameter + 1),      1.4259465903046195 / (type::diameter + 1),      1.4226110653753316 / (type::diameter + 1),      1.4192757356479440 / (type::diameter + 1),      1.4159405273780803 / (type::diameter + 1),      1.4126053666681344 / (type::diameter + 1),      1.4092701794546478 / (type::diameter + 1),      1.4059348914955811 / (type::diameter + 1),
                1.4025994283574768 / (type::diameter + 1),      1.3992637154025044 / (type::diameter + 1),      1.3959276777753835 / (type::diameter + 1),      1.3925912403901770 / (type::diameter + 1),      1.3892543279169491 / (type::diameter + 1),      1.3859168647682801 / (type::diameter + 1),      1.3825787750856321 / (type::diameter + 1),      1.3792399827255585 / (type::diameter + 1),
                1.3759004112457492 / (type::diameter + 1),      1.3725599838909057 / (type::diameter + 1),      1.3692186235784370 / (type::diameter + 1),      1.3658762528839699 / (type::diameter + 1),      1.3625327940266654 / (type::diameter + 1),      1.3591881688543321 / (type::diameter + 1),      1.3558422988283305 / (type::diameter + 1),      1.3524951050082579 / (type::diameter + 1),
                1.3491465080364050 / (type::diameter + 1),      1.3457964281219778 / (type::diameter + 1),      1.3424447850250714 / (type::diameter + 1),      1.3390914980403911 / (type::diameter + 1),      1.3357364859807063 / (type::diameter + 1),      1.3323796671600313 / (type::diameter + 1),      1.3290209593765195 / (type::diameter + 1),      1.3256602798950626 / (type::diameter + 1),
                1.3222975454295825 / (type::diameter + 1),      1.3189326721250059 / (type::diameter + 1),      1.3155655755389076 / (type::diameter + 1),      1.3121961706228144 / (type::diameter + 1),      1.3088243717031530 / (type::diameter + 1),      1.3054500924618322 / (type::diameter + 1),      1.3020732459164446 / (type::diameter + 1),      1.2986937444000756 / (type::diameter + 1),
                1.2953114995407035 / (type::diameter + 1),      1.2919264222401785 / (type::diameter + 1),      1.2885384226527642 / (type::diameter + 1),      1.2851474101632264 / (type::diameter + 1),      1.2817532933644530 / (type::diameter + 1),      1.2783559800345888 / (type::diameter + 1),      1.2749553771136677 / (type::diameter + 1),      1.2715513906797238 / (type::diameter + 1),
                1.2681439259243646 / (type::diameter + 1),      1.2647328871277857 / (type::diameter + 1),      1.2613181776332072 / (type::diameter + 1),      1.2578996998207125 / (type::diameter + 1),      1.2544773550804666 / (type::diameter + 1),      1.2510510437852929 / (type::diameter + 1),      1.2476206652625854 / (type::diameter + 1),      1.2441861177655313 / (type::diameter + 1),
                1.2407472984436212 / (type::diameter + 1),      1.2373041033124196 / (type::diameter + 1),      1.2338564272225693 / (type::diameter + 1),      1.2304041638280032 / (type::diameter + 1),      1.2269472055533323 / (type::diameter + 1),      1.2234854435603823 / (type::diameter + 1),      1.2200187677138457 / (type::diameter + 1),      1.2165470665460188 / (type::diameter + 1),
                1.2130702272205869 / (type::diameter + 1),      1.2095881354954267 / (type::diameter + 1),      1.2061006756843844 / (type::diameter + 1),      1.2026077306179960 / (type::diameter + 1),      1.1991091816031061 / (type::diameter + 1),      1.1956049083813462 / (type::diameter + 1),      1.1920947890864287 / (type::diameter + 1),      1.1885787002002105 / (type::diameter + 1),
                1.1850565165074805 / (type::diameter + 1),      1.1815281110494211 / (type::diameter + 1),      1.1779933550756928 / (type::diameter + 1),      1.1744521179950877 / (type::diameter + 1),      1.1709042673246970 / (type::diameter + 1),      1.1673496686375333 / (type::diameter + 1),      1.1637881855085470 / (type::diameter + 1),      1.1602196794589722 / (type::diameter + 1),
                1.1566440098989368 / (type::diameter + 1),      1.1530610340682651 / (type::diameter + 1),      1.1494706069754009 / (type::diameter + 1),      1.1458725813343748 / (type::diameter + 1),      1.1422668074997339 / (type::diameter + 1),      1.1386531333993515 / (type::diameter + 1),      1.1350314044650283 / (type::diameter + 1),      1.1314014635607919 / (type::diameter + 1),
                1.1277631509087991 / (type::diameter + 1),      1.1241163040127380 / (type::diameter + 1),      1.1204607575786250 / (type::diameter + 1),      1.1167963434328824 / (type::diameter + 1),      1.1131228904375819 / (type::diameter + 1),      1.1094402244027277 / (type::diameter + 1),      1.1057481679954507 / (type::diameter + 1),      1.1020465406459779 / (type::diameter + 1),
                1.0983351584502320 / (type::diameter + 1),      1.0946138340689101 / (type::diameter + 1),      1.0908823766228843 / (type::diameter + 1),      1.0871405915847540 / (type::diameter + 1),      1.0833882806663750 / (type::diameter + 1),      1.0796252417021791 / (type::diameter + 1),      1.0758512685280875 / (type::diameter + 1),      1.0720661508558112 / (type::diameter + 1),
                1.0682696741423201 / (type::diameter + 1),      1.0644616194542495 / (type::diameter + 1),      1.0606417633270015 / (type::diameter + 1),      1.0568098776182818 / (type::diameter + 1),      1.0529657293558021 / (type::diameter + 1),      1.0491090805788573 / (type::diameter + 1),      1.0452396881734747 / (type::diameter + 1),      1.0413573037008119 / (type::diameter + 1),
                1.0374616732184601 / (type::diameter + 1),      1.0335525370942926 / (type::diameter + 1),      1.0296296298124721 / (type::diameter + 1),      1.0256926797712092 / (type::diameter + 1),      1.0217414090718413 / (type::diameter + 1),      1.0177755332987681 / (type::diameter + 1),      1.0137947612897587 / (type::diameter + 1),      1.0097987948961083 / (type::diameter + 1),
                1.0057873287320922 / (type::diameter + 1),      1.0017600499131289 / (type::diameter + 1),      9.9771663778202386e-1 / (type::diameter + 1),   9.9365676362262742e-1 / (type::diameter + 1),   9.8958009036019242e-1 / (type::diameter + 1),   9.8548627224767178e-1 / (type::diameter + 1),   9.8137495453714329e-1 / (type::diameter + 1),   9.7724577313549378e-1 / (type::diameter + 1),
                9.7309835424343434e-1 / (type::diameter + 1),   9.6893231397685361e-1 / (type::diameter + 1),   9.6474725796944561e-1 / (type::diameter + 1),   9.6054278095547278e-1 / (type::diameter + 1),   9.5631846633144233e-1 / (type::diameter + 1),   9.5207388569538497e-1 / (type::diameter + 1),   9.4780859836232798e-1 / (type::diameter + 1),   9.4352215085444960e-1 / (type::diameter + 1),
                9.3921407636428721e-1 / (type::diameter + 1),   9.3488389418924775e-1 / (type::diameter + 1),   9.3053110913553288e-1 / (type::diameter + 1),   9.2615521088944445e-1 / (type::diameter + 1),   9.2175567335387426e-1 / (type::diameter + 1),   9.1733195394760656e-1 / (type::diameter + 1),   9.1288349286486954e-1 / (type::diameter + 1),   9.0840971229236151e-1 / (type::diameter + 1),
                9.0391001558074722e-1 / (type::diameter + 1),   8.9938378636736689e-1 / (type::diameter + 1),   8.9483038764662324e-1 / (type::diameter + 1),   8.9024916078420654e-1 / (type::diameter + 1),   8.8563942447098232e-1 / (type::diameter + 1),   8.8100047361199640e-1 / (type::diameter + 1),   8.7633157814564388e-1 / (type::diameter + 1),   8.7163198178759812e-1 / (type::diameter + 1),
                8.6690090069359742e-1 / (type::diameter + 1),   8.6213752203463460e-1 / (type::diameter + 1),   8.5734100247748310e-1 / (type::diameter + 1),   8.5251046656281246e-1 / (type::diameter + 1),   8.4764500497239050e-1 / (type::diameter + 1),   8.4274367267602633e-1 / (type::diameter + 1),   8.3780548694796916e-1 / (type::diameter + 1),   8.3282942524142711e-1 / (type::diameter + 1),
                8.2781442290869528e-1 / (type::diameter + 1),   8.2275937075306456e-1 / (type::diameter + 1),   8.1766311239720276e-1 / (type::diameter + 1),   8.1252444145103524e-1 / (type::diameter + 1),   8.0734209846027550e-1 / (type::diameter + 1),   8.0211476761463789e-1 / (type::diameter + 1),   7.9684107319236703e-1 / (type::diameter + 1),   7.9151957571500099e-1 / (type::diameter + 1),
                7.8614876778319769e-1 / (type::diameter + 1),   7.8072706956093855e-1 / (type::diameter + 1),   7.7525282387141246e-1 / (type::diameter + 1),   7.6972429086329515e-1 / (type::diameter + 1),   7.6413964220087982e-1 / (type::diameter + 1),   7.5849695472546989e-1 / (type::diameter + 1),   7.5279420352847999e-1 / (type::diameter + 1),   7.4702925436864418e-1 / (type::diameter + 1),
                7.4119985535640807e-1 / (type::diameter + 1),   7.3530362781775002e-1 / (type::diameter + 1),   7.2933805623705432e-1 / (type::diameter + 1),   7.2330047716390393e-1 / (type::diameter + 1),   7.1718806695135605e-1 / (type::diameter + 1),   7.1099782817290079e-1 / (type::diameter + 1),   7.0472657454125688e-1 / (type::diameter + 1),   6.9837091412365693e-1 / (type::diameter + 1),
                6.9192723061436353e-1 / (type::diameter + 1),   6.8539166238464561e-1 / (type::diameter + 1),   6.7876007898184343e-1 / (type::diameter + 1),   6.7202805469058628e-1 / (type::diameter + 1),   6.6519083869832794e-1 / (type::diameter + 1),   6.5824332132111363e-1 / (type::diameter + 1),   6.5117999564002287e-1 / (type::diameter + 1),   6.4399491376906305e-1 / (type::diameter + 1),
                6.3668163681495120e-1 / (type::diameter + 1),   6.2923317738976046e-1 / (type::diameter + 1),   6.2164193328768472e-1 / (type::diameter + 1),   6.1389961062239262e-1 / (type::diameter + 1),   6.0599713432177939e-1 / (type::diameter + 1),   5.9792454336558270e-1 / (type::diameter + 1),   5.8967086749171697e-1 / (type::diameter + 1),   5.8122398123882471e-1 / (type::diameter + 1),
                5.7257043006502768e-1 / (type::diameter + 1),   5.6369522178677684e-1 / (type::diameter + 1),   5.5458157457489263e-1 / (type::diameter + 1),   5.4521061002124009e-1 / (type::diameter + 1),   5.3556097604563260e-1 / (type::diameter + 1),   5.2560837919470082e-1 / (type::diameter + 1),   5.1532499850163813e-1 / (type::diameter + 1),   5.0467874245534135e-1 / (type::diameter + 1),
                4.9363229506874705e-1 / (type::diameter + 1),   4.8214187377839369e-1 / (type::diameter + 1),   4.7015558635112077e-1 / (type::diameter + 1),   4.5761121823148548e-1 / (type::diameter + 1),   4.4443319185881793e-1 / (type::diameter + 1),   4.3052828972059037e-1 / (type::diameter + 1),   4.1577947401088002e-1 / (type::diameter + 1),   4.0003666850050176e-1 / (type::diameter + 1),
                3.8310248105129543e-1 / (type::diameter + 1),   3.6470905546562093e-1 / (type::diameter + 1),   3.4447835352767045e-1 / (type::diameter + 1),   3.2184890256690199e-1 / (type::diameter + 1),   2.9592714272092498e-1 / (type::diameter + 1),   2.6514267174790225e-1 / (type::diameter + 1),   2.2626870482801179e-1 / (type::diameter + 1),   1.7041758857748693e-1 / (type::diameter + 1),
                -1.7041758857748693e-1 / (type::diameter + 1),  -2.2626870482801179e-1 / (type::diameter + 1),  -2.6514267174790225e-1 / (type::diameter + 1),  -2.9592714272092498e-1 / (type::diameter + 1),  -3.2184890256690199e-1 / (type::diameter + 1),  -3.4447835352767045e-1 / (type::diameter + 1),  -3.6470905546562093e-1 / (type::diameter + 1),  -3.8310248105129543e-1 / (type::diameter + 1),
                -4.0003666850050176e-1 / (type::diameter + 1),  -4.1577947401088002e-1 / (type::diameter + 1),  -4.3052828972059037e-1 / (type::diameter + 1),  -4.4443319185881793e-1 / (type::diameter + 1),  -4.5761121823148548e-1 / (type::diameter + 1),  -4.7015558635112077e-1 / (type::diameter + 1),  -4.8214187377839369e-1 / (type::diameter + 1),  -4.9363229506874705e-1 / (type::diameter + 1),
                -5.0467874245534135e-1 / (type::diameter + 1),  -5.1532499850163813e-1 / (type::diameter + 1),  -5.2560837919470082e-1 / (type::diameter + 1),  -5.3556097604563260e-1 / (type::diameter + 1),  -5.4521061002124009e-1 / (type::diameter + 1),  -5.5458157457489263e-1 / (type::diameter + 1),  -5.6369522178677684e-1 / (type::diameter + 1),  -5.7257043006502768e-1 / (type::diameter + 1),
                -5.8122398123882471e-1 / (type::diameter + 1),  -5.8967086749171697e-1 / (type::diameter + 1),  -5.9792454336558270e-1 / (type::diameter + 1),  -6.0599713432177939e-1 / (type::diameter + 1),  -6.1389961062239262e-1 / (type::diameter + 1),  -6.2164193328768472e-1 / (type::diameter + 1),  -6.2923317738976046e-1 / (type::diameter + 1),  -6.3668163681495120e-1 / (type::diameter + 1),
                -6.4399491376906305e-1 / (type::diameter + 1),  -6.5117999564002287e-1 / (type::diameter + 1),  -6.5824332132111363e-1 / (type::diameter + 1),  -6.6519083869832794e-1 / (type::diameter + 1),  -6.7202805469058628e-1 / (type::diameter + 1),  -6.7876007898184343e-1 / (type::diameter + 1),  -6.8539166238464561e-1 / (type::diameter + 1),  -6.9192723061436353e-1 / (type::diameter + 1),
                -6.9837091412365693e-1 / (type::diameter + 1),  -7.0472657454125688e-1 / (type::diameter + 1),  -7.1099782817290079e-1 / (type::diameter + 1),  -7.1718806695135605e-1 / (type::diameter + 1),  -7.2330047716390393e-1 / (type::diameter + 1),  -7.2933805623705432e-1 / (type::diameter + 1),  -7.3530362781775002e-1 / (type::diameter + 1),  -7.4119985535640807e-1 / (type::diameter + 1),
                -7.4702925436864418e-1 / (type::diameter + 1),  -7.5279420352847999e-1 / (type::diameter + 1),  -7.5849695472546989e-1 / (type::diameter + 1),  -7.6413964220087982e-1 / (type::diameter + 1),  -7.6972429086329515e-1 / (type::diameter + 1),  -7.7525282387141246e-1 / (type::diameter + 1),  -7.8072706956093855e-1 / (type::diameter + 1),  -7.8614876778319769e-1 / (type::diameter + 1),
                -7.9151957571500099e-1 / (type::diameter + 1),  -7.9684107319236703e-1 / (type::diameter + 1),  -8.0211476761463789e-1 / (type::diameter + 1),  -8.0734209846027550e-1 / (type::diameter + 1),  -8.1252444145103524e-1 / (type::diameter + 1),  -8.1766311239720276e-1 / (type::diameter + 1),  -8.2275937075306456e-1 / (type::diameter + 1),  -8.2781442290869528e-1 / (type::diameter + 1),
                -8.3282942524142711e-1 / (type::diameter + 1),  -8.3780548694796916e-1 / (type::diameter + 1),  -8.4274367267602633e-1 / (type::diameter + 1),  -8.4764500497239050e-1 / (type::diameter + 1),  -8.5251046656281246e-1 / (type::diameter + 1),  -8.5734100247748310e-1 / (type::diameter + 1),  -8.6213752203463460e-1 / (type::diameter + 1),  -8.6690090069359742e-1 / (type::diameter + 1),
                -8.7163198178759812e-1 / (type::diameter + 1),  -8.7633157814564388e-1 / (type::diameter + 1),  -8.8100047361199640e-1 / (type::diameter + 1),  -8.8563942447098232e-1 / (type::diameter + 1),  -8.9024916078420654e-1 / (type::diameter + 1),  -8.9483038764662324e-1 / (type::diameter + 1),  -8.9938378636736689e-1 / (type::diameter + 1),  -9.0391001558074722e-1 / (type::diameter + 1),
                -9.0840971229236151e-1 / (type::diameter + 1),  -9.1288349286486954e-1 / (type::diameter + 1),  -9.1733195394760656e-1 / (type::diameter + 1),  -9.2175567335387426e-1 / (type::diameter + 1),  -9.2615521088944445e-1 / (type::diameter + 1),  -9.3053110913553288e-1 / (type::diameter + 1),  -9.3488389418924775e-1 / (type::diameter + 1),  -9.3921407636428721e-1 / (type::diameter + 1),
                -9.4352215085444960e-1 / (type::diameter + 1),  -9.4780859836232798e-1 / (type::diameter + 1),  -9.5207388569538497e-1 / (type::diameter + 1),  -9.5631846633144233e-1 / (type::diameter + 1),  -9.6054278095547278e-1 / (type::diameter + 1),  -9.6474725796944561e-1 / (type::diameter + 1),  -9.6893231397685361e-1 / (type::diameter + 1),  -9.7309835424343434e-1 / (type::diameter + 1),
                -9.7724577313549378e-1 / (type::diameter + 1),  -9.8137495453714329e-1 / (type::diameter + 1),  -9.8548627224767178e-1 / (type::diameter + 1),  -9.8958009036019242e-1 / (type::diameter + 1),  -9.9365676362262742e-1 / (type::diameter + 1),  -9.9771663778202386e-1 / (type::diameter + 1),  -1.0017600499131289 / (type::diameter + 1),     -1.0057873287320922 / (type::diameter + 1),
                -1.0097987948961083 / (type::diameter + 1),     -1.0137947612897587 / (type::diameter + 1),     -1.0177755332987681 / (type::diameter + 1),     -1.0217414090718413 / (type::diameter + 1),     -1.0256926797712092 / (type::diameter + 1),     -1.0296296298124721 / (type::diameter + 1),     -1.0335525370942926 / (type::diameter + 1),     -1.0374616732184601 / (type::diameter + 1),
                -1.0413573037008119 / (type::diameter + 1),     -1.0452396881734747 / (type::diameter + 1),     -1.0491090805788573 / (type::diameter + 1),     -1.0529657293558021 / (type::diameter + 1),     -1.0568098776182818 / (type::diameter + 1),     -1.0606417633270015 / (type::diameter + 1),     -1.0644616194542495 / (type::diameter + 1),     -1.0682696741423201 / (type::diameter + 1),
                -1.0720661508558112 / (type::diameter + 1),     -1.0758512685280875 / (type::diameter + 1),     -1.0796252417021791 / (type::diameter + 1),     -1.0833882806663750 / (type::diameter + 1),     -1.0871405915847540 / (type::diameter + 1),     -1.0908823766228843 / (type::diameter + 1),     -1.0946138340689101 / (type::diameter + 1),     -1.0983351584502320 / (type::diameter + 1),
                -1.1020465406459779 / (type::diameter + 1),     -1.1057481679954507 / (type::diameter + 1),     -1.1094402244027277 / (type::diameter + 1),     -1.1131228904375819 / (type::diameter + 1),     -1.1167963434328824 / (type::diameter + 1),     -1.1204607575786250 / (type::diameter + 1),     -1.1241163040127380 / (type::diameter + 1),     -1.1277631509087991 / (type::diameter + 1),
                -1.1314014635607919 / (type::diameter + 1),     -1.1350314044650283 / (type::diameter + 1),     -1.1386531333993515 / (type::diameter + 1),     -1.1422668074997339 / (type::diameter + 1),     -1.1458725813343748 / (type::diameter + 1),     -1.1494706069754009 / (type::diameter + 1),     -1.1530610340682651 / (type::diameter + 1),     -1.1566440098989368 / (type::diameter + 1),
                -1.1602196794589722 / (type::diameter + 1),     -1.1637881855085470 / (type::diameter + 1),     -1.1673496686375333 / (type::diameter + 1),     -1.1709042673246970 / (type::diameter + 1),     -1.1744521179950877 / (type::diameter + 1),     -1.1779933550756928 / (type::diameter + 1),     -1.1815281110494211 / (type::diameter + 1),     -1.1850565165074805 / (type::diameter + 1),
                -1.1885787002002105 / (type::diameter + 1),     -1.1920947890864287 / (type::diameter + 1),     -1.1956049083813462 / (type::diameter + 1),     -1.1991091816031061 / (type::diameter + 1),     -1.2026077306179960 / (type::diameter + 1),     -1.2061006756843844 / (type::diameter + 1),     -1.2095881354954267 / (type::diameter + 1),     -1.2130702272205869 / (type::diameter + 1),
                -1.2165470665460188 / (type::diameter + 1),     -1.2200187677138457 / (type::diameter + 1),     -1.2234854435603823 / (type::diameter + 1),     -1.2269472055533323 / (type::diameter + 1),     -1.2304041638280032 / (type::diameter + 1),     -1.2338564272225693 / (type::diameter + 1),     -1.2373041033124196 / (type::diameter + 1),     -1.2407472984436212 / (type::diameter + 1),
                -1.2441861177655313 / (type::diameter + 1),     -1.2476206652625854 / (type::diameter + 1),     -1.2510510437852929 / (type::diameter + 1),     -1.2544773550804666 / (type::diameter + 1),     -1.2578996998207125 / (type::diameter + 1),     -1.2613181776332072 / (type::diameter + 1),     -1.2647328871277857 / (type::diameter + 1),     -1.2681439259243646 / (type::diameter + 1),
                -1.2715513906797238 / (type::diameter + 1),     -1.2749553771136677 / (type::diameter + 1),     -1.2783559800345888 / (type::diameter + 1),     -1.2817532933644530 / (type::diameter + 1),     -1.2851474101632264 / (type::diameter + 1),     -1.2885384226527642 / (type::diameter + 1),     -1.2919264222401785 / (type::diameter + 1),     -1.2953114995407035 / (type::diameter + 1),
                -1.2986937444000756 / (type::diameter + 1),     -1.3020732459164446 / (type::diameter + 1),     -1.3054500924618322 / (type::diameter + 1),     -1.3088243717031530 / (type::diameter + 1),     -1.3121961706228144 / (type::diameter + 1),     -1.3155655755389076 / (type::diameter + 1),     -1.3189326721250059 / (type::diameter + 1),     -1.3222975454295825 / (type::diameter + 1),
                -1.3256602798950626 / (type::diameter + 1),     -1.3290209593765195 / (type::diameter + 1),     -1.3323796671600313 / (type::diameter + 1),     -1.3357364859807063 / (type::diameter + 1),     -1.3390914980403911 / (type::diameter + 1),     -1.3424447850250714 / (type::diameter + 1),     -1.3457964281219778 / (type::diameter + 1),     -1.3491465080364050 / (type::diameter + 1),
                -1.3524951050082579 / (type::diameter + 1),     -1.3558422988283305 / (type::diameter + 1),     -1.3591881688543321 / (type::diameter + 1),     -1.3625327940266654 / (type::diameter + 1),     -1.3658762528839699 / (type::diameter + 1),     -1.3692186235784370 / (type::diameter + 1),     -1.3725599838909057 / (type::diameter + 1),     -1.3759004112457492 / (type::diameter + 1),
                -1.3792399827255585 / (type::diameter + 1),     -1.3825787750856321 / (type::diameter + 1),     -1.3859168647682801 / (type::diameter + 1),     -1.3892543279169491 / (type::diameter + 1),     -1.3925912403901770 / (type::diameter + 1),     -1.3959276777753835 / (type::diameter + 1),     -1.3992637154025044 / (type::diameter + 1),     -1.4025994283574768 / (type::diameter + 1),
                -1.4059348914955811 / (type::diameter + 1),     -1.4092701794546478 / (type::diameter + 1),     -1.4126053666681344 / (type::diameter + 1),     -1.4159405273780803 / (type::diameter + 1),     -1.4192757356479440 / (type::diameter + 1),     -1.4226110653753316 / (type::diameter + 1),     -1.4259465903046195 / (type::diameter + 1),     -1.4292823840394803 / (type::diameter + 1),
                -1.4326185200553153 / (type::diameter + 1),     -1.4359550717116014 / (type::diameter + 1),     -1.4392921122641568 / (type::diameter + 1),     -1.4426297148773315 / (type::diameter + 1),     -1.4459679526361285 / (type::diameter + 1),     -1.4493068985582607 / (type::diameter + 1),     -1.4526466256061495 / (type::diameter + 1),     -1.4559872066988694 / (type::diameter + 1),
                -1.4593287147240453 / (type::diameter + 1),     -1.4626712225497066 / (type::diameter + 1),     -1.4660148030361038 / (type::diameter + 1),     -1.4693595290474926 / (type::diameter + 1),     -1.4727054734638911 / (type::diameter + 1),     -1.4760527091928140 / (type::diameter + 1),     -1.4794013091809903 / (type::diameter + 1),     -1.4827513464260682 / (type::diameter + 1),
                -1.4861028939883133 / (type::diameter + 1),     -1.4894560250023045 / (type::diameter + 1),     -1.4928108126886319 / (type::diameter + 1),     -1.4961673303656038 / (type::diameter + 1),     -1.4995256514609645 / (type::diameter + 1),     -1.5028858495236314 / (type::diameter + 1),     -1.5062479982354535 / (type::diameter + 1),     -1.5096121714229974 / (type::diameter + 1),
                -1.5129784430693663 / (type::diameter + 1),     -1.5163468873260558 / (type::diameter + 1),     -1.5197175785248521 / (type::diameter + 1),     -1.5230905911897777 / (type::diameter + 1),     -1.5264660000490895 / (type::diameter + 1),     -1.5298438800473342 / (type::diameter + 1),     -1.5332243063574660 / (type::diameter + 1),     -1.5366073543930328 / (type::diameter + 1),
                -1.5399930998204339 / (type::diameter + 1),     -1.5433816185712570 / (type::diameter + 1),     -1.5467729868546979 / (type::diameter + 1),     -1.5501672811700688 / (type::diameter + 1),     -1.5535645783194007 / (type::diameter + 1),     -1.5569649554201453 / (type::diameter + 1),     -1.5603684899179821 / (type::diameter + 1),     -1.5637752595997354 / (type::diameter + 1),
                -1.5671853426064083 / (type::diameter + 1),     -1.5705988174463378 / (type::diameter + 1),     -1.5740157630084784 / (type::diameter + 1),     -1.5774362585758194 / (type::diameter + 1),     -1.5808603838389411 / (type::diameter + 1),     -1.5842882189097174 / (type::diameter + 1),     -1.5877198443351710 / (type::diameter + 1),     -1.5911553411114858 / (type::diameter + 1),
                -1.5945947906981849 / (type::diameter + 1),     -1.5980382750324798 / (type::diameter + 1),     -1.6014858765437981 / (type::diameter + 1),     -1.6049376781684953 / (type::diameter + 1),     -1.6083937633647595 / (type::diameter + 1),     -1.6118542161277145 / (type::diameter + 1),     -1.6153191210047294 / (type::diameter + 1),     -1.6187885631109426 / (type::diameter + 1),
                -1.6222626281450062 / (type::diameter + 1),     -1.6257414024050602 / (type::diameter + 1),     -1.6292249728049442 / (type::diameter + 1),     -1.6327134268906535 / (type::diameter + 1),     -1.6362068528570498 / (type::diameter + 1),     -1.6397053395648339 / (type::diameter + 1),     -1.6432089765577891 / (type::diameter + 1),     -1.6467178540803049 / (type::diameter + 1),
                -1.6502320630951906 / (type::diameter + 1),     -1.6537516953017864 / (type::diameter + 1),     -1.6572768431543845 / (type::diameter + 1),     -1.6608075998809673 / (type::diameter + 1),     -1.6643440595022755 / (type::diameter + 1),     -1.6678863168512151 / (type::diameter + 1),     -1.6714344675926146 / (type::diameter + 1),     -1.6749886082433434 / (type::diameter + 1),
                -1.6785488361928036 / (type::diameter + 1),     -1.6821152497238058 / (type::diameter + 1),     -1.6856879480338421 / (type::diameter + 1),     -1.6892670312567682 / (type::diameter + 1),     -1.6928526004849079 / (type::diameter + 1),     -1.6964447577915930 / (type::diameter + 1),     -1.7000436062541523 / (type::diameter + 1),     -1.7036492499773638 / (type::diameter + 1),
                -1.7072617941173850 / (type::diameter + 1),     -1.7108813449061757 / (type::diameter + 1),     -1.7145080096764288 / (type::diameter + 1),     -1.7181418968870262 / (type::diameter + 1),     -1.7217831161490343 / (type::diameter + 1),     -1.7254317782522580 / (type::diameter + 1),     -1.7290879951923689 / (type::diameter + 1),     -1.7327518801986285 / (type::diameter + 1),
                -1.7364235477622212 / (type::diameter + 1),     -1.7401031136652208 / (type::diameter + 1),     -1.7437906950102073 / (type::diameter + 1),     -1.7474864102505558 / (type::diameter + 1),     -1.7511903792214188 / (type::diameter + 1),     -1.7549027231714249 / (type::diameter + 1),     -1.7586235647951147 / (type::diameter + 1),     -1.7623530282661394 / (type::diameter + 1),
                -1.7660912392712462 / (type::diameter + 1),     -1.7698383250450752 / (type::diameter + 1),     -1.7735944144057943 / (type::diameter + 1),     -1.7773596377916004 / (type::diameter + 1),     -1.7811341272981129 / (type::diameter + 1),     -1.7849180167166913 / (type::diameter + 1),     -1.7887114415737045 / (type::diameter + 1),     -1.7925145391707853 / (type::diameter + 1),
                -1.7963274486261016 / (type::diameter + 1),     -1.8001503109166781 / (type::diameter + 1),     -1.8039832689218035 / (type::diameter + 1),     -1.8078264674675599 / (type::diameter + 1),     -1.8116800533725120 / (type::diameter + 1),     -1.8155441754945940 / (type::diameter + 1),     -1.8194189847792369 / (type::diameter + 1),     -1.8233046343087771 / (type::diameter + 1),
                -1.8272012793531899 / (type::diameter + 1),     -1.8311090774221942 / (type::diameter + 1),     -1.8350281883187756 / (type::diameter + 1),     -1.8389587741941765 / (type::diameter + 1),     -1.8429009996044052 / (type::diameter + 1),     -1.8468550315683164 / (type::diameter + 1),     -1.8508210396273195 / (type::diameter + 1),     -1.8547991959067708 / (type::diameter + 1),
                -1.8587896751791113 / (type::diameter + 1),     -1.8627926549288112 / (type::diameter + 1),     -1.8668083154191869 / (type::diameter + 1),     -1.8708368397611575 / (type::diameter + 1),     -1.8748784139840128 / (type::diameter + 1),     -1.8789332271082637 / (type::diameter + 1),     -1.8830014712206555 / (type::diameter + 1),     -1.8870833415514195 / (type::diameter + 1),
                -1.8911790365538510 / (type::diameter + 1),     -1.8952887579862965 / (type::diameter + 1),     -1.8994127109966441 / (type::diameter + 1),     -1.9035511042094096 / (type::diameter + 1),     -1.9077041498155190 / (type::diameter + 1),     -1.9118720636648895 / (type::diameter + 1),     -1.9160550653619177 / (type::diameter + 1),     -1.9202533783639877 / (type::diameter + 1),
                -1.9244672300831170 / (type::diameter + 1),     -1.9286968519908639 / (type::diameter + 1),     -1.9329424797266246 / (type::diameter + 1),     -1.9372043532094561 / (type::diameter + 1),     -1.9414827167535663 / (type::diameter + 1),     -1.9457778191876175 / (type::diameter + 1),     -1.9500899139780004 / (type::diameter + 1),     -1.9544192593562404 / (type::diameter + 1),
                -1.9587661184507046 / (type::diameter + 1),     -1.9631307594227913 / (type::diameter + 1),     -1.9675134556077848 / (type::diameter + 1),     -1.9719144856605762 / (type::diameter + 1),     -1.9763341337064515 / (type::diameter + 1),     -1.9807726894971676 / (type::diameter + 1),     -1.9852304485725390 / (type::diameter + 1),     -1.9897077124277773 / (type::diameter + 1),
                -1.9942047886868308 / (type::diameter + 1),     -1.9987219912819901 / (type::diameter + 1),     -2.0032596406400350 / (type::diameter + 1),     -2.0078180638752146 / (type::diameter + 1),     -2.0123975949893673 / (type::diameter + 1),     -2.0169985750795031 / (type::diameter + 1),     -2.0216213525531890 / (type::diameter + 1),     -2.0262662833520941 / (type::diameter + 1),
                -2.0309337311840735 / (type::diameter + 1),     -2.0356240677641887 / (type::diameter + 1),     -2.0403376730650835 / (type::diameter + 1),     -2.0450749355771602 / (type::diameter + 1),     -2.0498362525790223 / (type::diameter + 1),     -2.0546220304186797 / (type::diameter + 1),     -2.0594326848060371 / (type::diameter + 1),     -2.0642686411172195 / (type::diameter + 1),
                -2.0691303347113164 / (type::diameter + 1),     -2.0740182112601659 / (type::diameter + 1),     -2.0789327270918298 / (type::diameter + 1),     -2.0838743495484545 / (type::diameter + 1),     -2.0888435573592524 / (type::diameter + 1),     -2.0938408410293801 / (type::diameter + 1),     -2.0988667032455423 / (type::diameter + 1),     -2.1039216592991946 / (type::diameter + 1),
                -2.1090062375282789 / (type::diameter + 1),     -2.1141209797784779 / (type::diameter + 1),     -2.1192664418850403 / (type::diameter + 1),     -2.1244431941762954 / (type::diameter + 1),     -2.1296518220000450 / (type::diameter + 1),     -2.1348929262740997 / (type::diameter + 1),     -2.1401671240623097 / (type::diameter + 1),     -2.1454750491775266 / (type::diameter + 1),
                -2.1508173528130321 / (type::diameter + 1),     -2.1561947042040695 / (type::diameter + 1),     -2.1616077913212271 / (type::diameter + 1),     -2.1670573215975428 / (type::diameter + 1),     -2.1725440226913261 / (type::diameter + 1),     -2.1780686432868369 / (type::diameter + 1),     -2.1836319539351109 / (type::diameter + 1),     -2.1892347479373814 / (type::diameter + 1),
                -2.1948778422737315 / (type::diameter + 1),     -2.2005620785797949 / (type::diameter + 1),     -2.2062883241745377 / (type::diameter + 1),     -2.2120574731423764 / (type::diameter + 1),     -2.2178704474731334 / (type::diameter + 1),     -2.2237281982635985 / (type::diameter + 1),     -2.2296317069847555 / (type::diameter + 1),     -2.2355819868190481 / (type::diameter + 1),
                -2.2415800840724064 / (type::diameter + 1),     -2.2476270796661295 / (type::diameter + 1),     -2.2537240907141323 / (type::diameter + 1),     -2.2598722721915137 / (type::diameter + 1),     -2.2660728187008963 / (type::diameter + 1),     -2.2723269663435255 / (type::diameter + 1),     -2.2786359947027097 / (type::diameter + 1),     -2.2850012289478306 / (type::diameter + 1),
                -2.2914240420678696 / (type::diameter + 1),     -2.2979058572441794 / (type::diameter + 1),     -2.3044481503730991 / (type::diameter + 1),     -2.3110524527499645 / (type::diameter + 1),     -2.3177203539271236 / (type::diameter + 1),     -2.3244535047597318 / (type::diameter + 1),     -2.3312536206543983 / (type::diameter + 1),     -2.3381224850371873 / (type::diameter + 1),
                -2.3450619530590706 / (type::diameter + 1),     -2.3520739555587000 / (type::diameter + 1),     -2.3591605033043417 / (type::diameter + 1),     -2.3663236915390124 / (type::diameter + 1),     -2.3735657048553191 / (type::diameter + 1),     -2.3808888224292500 / (type::diameter + 1),     -2.3882954236452498 / (type::diameter + 1),     -2.3957879941483700 / (type::diameter + 1),
                -2.4033691323631760 / (type::diameter + 1),     -2.4110415565234738 / (type::diameter + 1),     -2.4188081122618657 / (type::diameter + 1),     -2.4266717808137350 / (type::diameter + 1),     -2.4346356878965929 / (type::diameter + 1),     -2.4427031133329121 / (type::diameter + 1),     -2.4508775014927480 / (type::diameter + 1),     -2.4591624726417722 / (type::diameter + 1),
                -2.4675618352909908 / (type::diameter + 1),     -2.4760795996566162 / (type::diameter + 1),     -2.4847199923525551 / (type::diameter + 1),     -2.4934874724540813 / (type::diameter + 1),     -2.5023867490898326 / (type::diameter + 1),     -2.5114228007407585 / (type::diameter + 1),     -2.5206008964495547 / (type::diameter + 1),     -2.5299266191730942 / (type::diameter + 1),
                -2.5394058915441638 / (type::diameter + 1),     -2.5490450043483498 / (type::diameter + 1),     -2.5588506480683336 / (type::diameter + 1),     -2.5688299479025083 / (type::diameter + 1),     -2.5789905027294192 / (type::diameter + 1),     -2.5893404285661339 / (type::diameter + 1),     -2.5998884071598398 / (type::diameter + 1),     -2.6106437404609705 / (type::diameter + 1),
                -2.6216164118569691 / (type::diameter + 1),     -2.6328171552034775 / (type::diameter + 1),     -2.6442575328806557 / (type::diameter + 1),     -2.6559500243346071 / (type::diameter + 1),     -2.6679081268478898 / (type::diameter + 1),     -2.6801464706321721 / (type::diameter + 1),     -2.6926809507675676 / (type::diameter + 1),     -2.7055288790496144 / (type::diameter + 1),
                -2.7187091594759438 / (type::diameter + 1),     -2.7322424919497175 / (type::diameter + 1),     -2.7461516098484305 / (type::diameter + 1),     -2.7604615584754485 / (type::diameter + 1),     -2.7752000231739453 / (type::diameter + 1),     -2.7903977181709911 / (type::diameter + 1),     -2.8060888502170392 / (type::diameter + 1),     -2.8223116750508611 / (type::diameter + 1),
                -2.8391091700186590 / (type::diameter + 1),     -2.8565298533366061 / (type::diameter + 1),     -2.8746287902796272 / (type::diameter + 1),     -2.8934688401496455 / (type::diameter + 1),     -2.9131222169485817 / (type::diameter + 1),     -2.9336724639032943 / (type::diameter + 1),     -2.9552169815083583 / (type::diameter + 1),     -2.9778703072041906 / (type::diameter + 1),
                -3.0017684330687534 / (type::diameter + 1),     -3.0270745842754689 / (type::diameter + 1),     -3.0539870972903128 / (type::diameter + 1),     -3.0827503897194092 / (type::diameter + 1),     -3.1136706092218944 / (type::diameter + 1),     -3.1471385926519712 / (type::diameter + 1),     -3.1836646787008854 / (type::diameter + 1),     -3.2239336074705574 / (type::diameter + 1),
                -3.2688953201247243 / (type::diameter + 1),     -3.3199242727525520 / (type::diameter + 1),     -3.3791208509098653 / (type::diameter + 1),     -3.4499415844581948 / (type::diameter + 1),     -3.5387147915535359 / (type::diameter + 1),     -3.6591529330911164 / (type::diameter + 1),     -3.8520461503683912 / (type::diameter + 1),     -4.0968586097934827 / (type::diameter + 1)
            };
            
            // (<diameter> + 1)-downscaled heights of the boxes: { f(x_1), f(x_2) - f(x_1), ..., f(x_{n - 2}) - f(x_{n - 1}), f(x_{n - 2}) }.
            const result_type  m_height_scaled[n_boxes] = {
                2.3923402393103877e-4 / (type::diameter + 1),   2.5443827317688897e-4 / (type::diameter + 1),   2.6785105422457909e-4 / (type::diameter + 1),   2.7696721223106476e-4 / (type::diameter + 1),   2.8409407716140791e-4 / (type::diameter + 1),   2.9004821488805630e-4 / (type::diameter + 1),   2.9521997798004228e-4 / (type::diameter + 1),   2.9982849700430920e-4 / (type::diameter + 1),
                3.0400997353862756e-4 / (type::diameter + 1),   3.0785527673641671e-4 / (type::diameter + 1),   3.1142828377047018e-4 / (type::diameter + 1),   3.1477574018092589e-4 / (type::diameter + 1),   3.1793296465583298e-4 / (type::diameter + 1),   3.2092734496718371e-4 / (type::diameter + 1),   3.2378058201430321e-4 / (type::diameter + 1),   3.2651018642881690e-4 / (type::diameter + 1),
                3.2913050925229932e-4 / (type::diameter + 1),   3.3165347141351495e-4 / (type::diameter + 1),   3.3408909234310643e-4 / (type::diameter + 1),   3.3644588098471659e-4 / (type::diameter + 1),   3.3873113029505674e-4 / (type::diameter + 1),   3.4095114263503813e-4 / (type::diameter + 1),   3.4311140475307431e-4 / (type::diameter + 1),   3.4521672538959636e-4 / (type::diameter + 1),
                3.4727134474960270e-4 / (type::diameter + 1),   3.4927902251620045e-4 / (type::diameter + 1),   3.5124310929405541e-4 / (type::diameter + 1),   3.5316660511428102e-4 / (type::diameter + 1),   3.5505220773250386e-4 / (type::diameter + 1),   3.5690235279890893e-4 / (type::diameter + 1),   3.5871924749915410e-4 / (type::diameter + 1),   3.6050489890810574e-4 / (type::diameter + 1),
                3.6226113802995295e-4 / (type::diameter + 1),   3.6398964029438007e-4 / (type::diameter + 1),   3.6569194312213691e-4 / (type::diameter + 1),   3.6736946105239587e-4 / (type::diameter + 1),   3.6902349882993822e-4 / (type::diameter + 1),   3.7065526277604515e-4 / (type::diameter + 1),   3.7226587070824085e-4 / (type::diameter + 1),   3.7385636062721188e-4 / (type::diameter + 1),
                3.7542769835165452e-4 / (type::diameter + 1),   3.7698078425146797e-4 / (type::diameter + 1),   3.7851645920507957e-4 / (type::diameter + 1),   3.8003550988657773e-4 / (type::diameter + 1),   3.8153867347182342e-4 / (type::diameter + 1),   3.8302664183909911e-4 / (type::diameter + 1),   3.8450006532857422e-4 / (type::diameter + 1),   3.8595955611547845e-4 / (type::diameter + 1),
                3.8740569124402679e-4 / (type::diameter + 1),   3.8883901536255420e-4 / (type::diameter + 1),   3.9026004319476904e-4 / (type::diameter + 1),   3.9166926177734152e-4 / (type::diameter + 1),   3.9306713249006123e-4 / (type::diameter + 1),   3.9445409290140627e-4 / (type::diameter + 1),   3.9583055844946910e-4 / (type::diameter + 1),   3.9719692397570074e-4 / (type::diameter + 1),
                3.9855356512680048e-4 / (type::diameter + 1),   3.9990083963823777e-4 / (type::diameter + 1),   4.0123908851130159e-4 / (type::diameter + 1),   4.0256863709419375e-4 / (type::diameter + 1),   4.0388979607648341e-4 / (type::diameter + 1),   4.0520286240519585e-4 / (type::diameter + 1),   4.0650812012989623e-4 / (type::diameter + 1),   4.0780584118333054e-4 / (type::diameter + 1),
                4.0909628610348510e-4 / (type::diameter + 1),   4.1037970470231012e-4 / (type::diameter + 1),   4.1165633668580967e-4 / (type::diameter + 1),   4.1292641222972120e-4 / (type::diameter + 1),   4.1419015251458370e-4 / (type::diameter + 1),   4.1544777022361763e-4 / (type::diameter + 1),   4.1669947000650592e-4 / (type::diameter + 1),   4.1794544891186846e-4 / (type::diameter + 1),
                4.1918589679095784e-4 / (type::diameter + 1),   4.2042099667486779e-4 / (type::diameter + 1),   4.2165092512733465e-4 / (type::diameter + 1),   4.2287585257502291e-4 / (type::diameter + 1),   4.2409594361701633e-4 / (type::diameter + 1),   4.2531135731508343e-4 / (type::diameter + 1),   4.2652224746614948e-4 / (type::diameter + 1),   4.2772876285828307e-4 / (type::diameter + 1),
                4.2893104751139428e-4 / (type::diameter + 1),   4.3012924090374053e-4 / (type::diameter + 1),   4.3132347818524530e-4 / (type::diameter + 1),   4.3251389037855221e-4 / (type::diameter + 1),   4.3370060456866239e-4 / (type::diameter + 1),   4.3488374408193496e-4 / (type::diameter + 1),   4.3606342865516862e-4 / (type::diameter + 1),   4.3723977459542654e-4 / (type::diameter + 1),
                4.3841289493121502e-4 / (type::diameter + 1),   4.3958289955558005e-4 / (type::diameter + 1),   4.4074989536164313e-4 / (type::diameter + 1),   4.4191398637105876e-4 / (type::diameter + 1),   4.4307527385584019e-4 / (type::diameter + 1),   4.4423385645396758e-4 / (type::diameter + 1),   4.4538983027916266e-4 / (type::diameter + 1),   4.4654328902518634e-4 / (type::diameter + 1),
                4.4769432406499070e-4 / (type::diameter + 1),   4.4884302454503342e-4 / (type::diameter + 1),   4.4998947747504148e-4 / (type::diameter + 1),   4.5113376781349093e-4 / (type::diameter + 1),   4.5227597854905195e-4 / (type::diameter + 1),   4.5341619077823109e-4 / (type::diameter + 1),   4.5455448377942754e-4 / (type::diameter + 1),   4.5569093508360579e-4 / (type::diameter + 1),
                4.5682562054177381e-4 / (type::diameter + 1),   4.5795861438944383e-4 / (type::diameter + 1),   4.5908998930824123e-4 / (type::diameter + 1),   4.6021981648481672e-4 / (type::diameter + 1),   4.6134816566720715e-4 / (type::diameter + 1),   4.6247510521878130e-4 / (type::diameter + 1),   4.6360070216989856e-4 / (type::diameter + 1),   4.6472502226740063e-4 / (type::diameter + 1),
                4.6584813002204898e-4 / (type::diameter + 1),   4.6697008875401429e-4 / (type::diameter + 1),   4.6809096063651749e-4 / (type::diameter + 1),   4.6921080673771644e-4 / (type::diameter + 1),   4.7032968706092645e-4 / (type::diameter + 1),   4.7144766058325818e-4 / (type::diameter + 1),   4.7256478529275122e-4 / (type::diameter + 1),   4.7368111822407756e-4 / (type::diameter + 1),
                4.7479671549288474e-4 / (type::diameter + 1),   4.7591163232884470e-4 / (type::diameter + 1),   4.7702592310747063e-4 / (type::diameter + 1),   4.7813964138076076e-4 / (type::diameter + 1),   4.7925283990672479e-4 / (type::diameter + 1),   4.8036557067784553e-4 / (type::diameter + 1),   4.8147788494852587e-4 / (type::diameter + 1),   4.8258983326156804e-4 / (type::diameter + 1),
                4.8370146547373007e-4 / (type::diameter + 1),   4.8481283078040182e-4 / (type::diameter + 1),   4.8592397773944079e-4 / (type::diameter + 1),   4.8703495429420585e-4 / (type::diameter + 1),   4.8814580779582513e-4 / (type::diameter + 1),   4.8925658502473245e-4 / (type::diameter + 1),   4.9036733221150491e-4 / (type::diameter + 1),   4.9147809505703283e-4 / (type::diameter + 1),
                4.9258891875205132e-4 / (type::diameter + 1),   4.9369984799606189e-4 / (type::diameter + 1),   4.9481092701567046e-4 / (type::diameter + 1),   4.9592219958236752e-4 / (type::diameter + 1),   4.9703370902977450e-4 / (type::diameter + 1),   4.9814549827037955e-4 / (type::diameter + 1),   4.9925760981178458e-4 / (type::diameter + 1),   5.0037008577248484e-4 / (type::diameter + 1),
                5.0148296789720071e-4 / (type::diameter + 1),   5.0259629757178118e-4 / (type::diameter + 1),   5.0371011583769701e-4 / (type::diameter + 1),   5.0482446340614116e-4 / (type::diameter + 1),   5.0593938067175309e-4 / (type::diameter + 1),   5.0705490772598294e-4 / (type::diameter + 1),   5.0817108437011072e-4 / (type::diameter + 1),   5.0928795012793528e-4 / (type::diameter + 1),
                5.1040554425814682e-4 / (type::diameter + 1),   5.1152390576639650e-4 / (type::diameter + 1),   5.1264307341707586e-4 / (type::diameter + 1),   5.1376308574481834e-4 / (type::diameter + 1),   5.1488398106573482e-4 / (type::diameter + 1),   5.1600579748839425e-4 / (type::diameter + 1),   5.1712857292456051e-4 / (type::diameter + 1),   5.1825234509969562e-4 / (type::diameter + 1),
                5.1937715156323961e-4 / (type::diameter + 1),   5.2050302969867644e-4 / (type::diameter + 1),   5.2163001673339541e-4 / (type::diameter + 1),   5.2275814974835682e-4 / (type::diameter + 1),   5.2388746568757051e-4 / (type::diameter + 1),   5.2501800136739568e-4 / (type::diameter + 1),   5.2614979348566963e-4 / (type::diameter + 1),   5.2728287863067345e-4 / (type::diameter + 1),
                5.2841729328994176e-4 / (type::diameter + 1),   5.2955307385892391e-4 / (type::diameter + 1),   5.3069025664950325e-4 / (type::diameter + 1),   5.3182887789838142e-4 / (type::diameter + 1),   5.3296897377533393e-4 / (type::diameter + 1),   5.3411058039134321e-4 / (type::diameter + 1),   5.3525373380661542e-4 / (type::diameter + 1),   5.3639847003848653e-4 / (type::diameter + 1),
                5.3754482506922359e-4 / (type::diameter + 1),   5.3869283485372654e-4 / (type::diameter + 1),   5.3984253532713596e-4 / (type::diameter + 1),   5.4099396241235180e-4 / (type::diameter + 1),   5.4214715202746834e-4 / (type::diameter + 1),   5.4330214009313000e-4 / (type::diameter + 1),   5.4445896253981295e-4 / (type::diameter + 1),   5.4561765531503707e-4 / (type::diameter + 1),
                5.4677825439051269e-4 / (type::diameter + 1),   5.4794079576922669e-4 / (type::diameter + 1),   5.4910531549247205e-4 / (type::diameter + 1),   5.5027184964682512e-4 / (type::diameter + 1),   5.5144043437107480e-4 / (type::diameter + 1),   5.5261110586310734e-4 / (type::diameter + 1),   5.5378390038675106e-4 / (type::diameter + 1),   5.5495885427858451e-4 / (type::diameter + 1),
                5.5613600395471194e-4 / (type::diameter + 1),   5.5731538591750988e-4 / (type::diameter + 1),   5.5849703676234821e-4 / (type::diameter + 1),   5.5968099318428951e-4 / (type::diameter + 1),   5.6086729198477013e-4 / (type::diameter + 1),   5.6205597007826628e-4 / (type::diameter + 1),   5.6324706449894880e-4 / (type::diameter + 1),   5.6444061240732972e-4 / (type::diameter + 1),
                5.6563665109690415e-4 / (type::diameter + 1),   5.6683521800079051e-4 / (type::diameter + 1),   5.6803635069837260e-4 / (type::diameter + 1),   5.6924008692194653e-4 / (type::diameter + 1),   5.7044646456337580e-4 / (type::diameter + 1),   5.7165552168075758e-4 / (type::diameter + 1),   5.7286729650510343e-4 / (type::diameter + 1),   5.7408182744703748e-4 / (type::diameter + 1),
                5.7529915310351519e-4 / (type::diameter + 1),   5.7651931226456585e-4 / (type::diameter + 1),   5.7774234392006167e-4 / (type::diameter + 1),   5.7896828726651686e-4 / (type::diameter + 1),   5.8019718171391938e-4 / (type::diameter + 1),   5.8142906689259872e-4 / (type::diameter + 1),   5.8266398266013263e-4 / (type::diameter + 1),   5.8390196910829579e-4 / (type::diameter + 1),
                5.8514306657005369e-4 / (type::diameter + 1),   5.8638731562660458e-4 / (type::diameter + 1),   5.8763475711447272e-4 / (type::diameter + 1),   5.8888543213265591e-4 / (type::diameter + 1),   5.9013938204983056e-4 / (type::diameter + 1),   5.9139664851161732e-4 / (type::diameter + 1),   5.9265727344791041e-4 / (type::diameter + 1),   5.9392129908027399e-4 / (type::diameter + 1),
                5.9518876792940856e-4 / (type::diameter + 1),   5.9645972282269079e-4 / (type::diameter + 1),   5.9773420690179000e-4 / (type::diameter + 1),   5.9901226363036458e-4 / (type::diameter + 1),   6.0029393680184167e-4 / (type::diameter + 1),   6.0157927054728360e-4 / (type::diameter + 1),   6.0286830934334433e-4 / (type::diameter + 1),   6.0416109802031955e-4 / (type::diameter + 1),
                6.0545768177029381e-4 / (type::diameter + 1),   6.0675810615538839e-4 / (type::diameter + 1),   6.0806241711611338e-4 / (type::diameter + 1),   6.0937066097982781e-4 / (type::diameter + 1),   6.1068288446931149e-4 / (type::diameter + 1),   6.1199913471145236e-4 / (type::diameter + 1),   6.1331945924605326e-4 / (type::diameter + 1),   6.1464390603476209e-4 / (type::diameter + 1),
                6.1597252347012929e-4 / (type::diameter + 1),   6.1730536038479682e-4 / (type::diameter + 1),   6.1864246606082280e-4 / (type::diameter + 1),   6.1998389023914601e-4 / (type::diameter + 1),   6.2132968312919466e-4 / (type::diameter + 1),   6.2267989541864385e-4 / (type::diameter + 1),   6.2403457828332623e-4 / (type::diameter + 1),   6.2539378339730049e-4 / (type::diameter + 1),
                6.2675756294308244e-4 / (type::diameter + 1),   6.2812596962204347e-4 / (type::diameter + 1),   6.2949905666498138e-4 / (type::diameter + 1),   6.3087687784286864e-4 / (type::diameter + 1),   6.3225948747778315e-4 / (type::diameter + 1),   6.3364694045402700e-4 / (type::diameter + 1),   6.3503929222943850e-4 / (type::diameter + 1),   6.3643659884690310e-4 / (type::diameter + 1),
                6.3783891694606889e-4 / (type::diameter + 1),   6.3924630377527255e-4 / (type::diameter + 1),   6.4065881720368174e-4 / (type::diameter + 1),   6.4207651573366000e-4 / (type::diameter + 1),   6.4349945851336063e-4 / (type::diameter + 1),   6.4492770534955582e-4 / (type::diameter + 1),   6.4636131672070786e-4 / (type::diameter + 1),   6.4780035379028910e-4 / (type::diameter + 1),
                6.4924487842035780e-4 / (type::diameter + 1),   6.5069495318539696e-4 / (type::diameter + 1),   6.5215064138642356e-4 / (type::diameter + 1),   6.5361200706537587e-4 / (type::diameter + 1),   6.5507911501978651e-4 / (type::diameter + 1),   6.5655203081774944e-4 / (type::diameter + 1),   6.5803082081318906e-4 / (type::diameter + 1),   6.5951555216143991e-4 / (type::diameter + 1),
                6.6100629283514575e-4 / (type::diameter + 1),   6.6250311164048702e-4 / (type::diameter + 1),   6.6400607823374590e-4 / (type::diameter + 1),   6.6551526313821857e-4 / (type::diameter + 1),   6.6703073776148440e-4 / (type::diameter + 1),   6.6855257441304227e-4 / (type::diameter + 1),   6.7008084632232438e-4 / (type::diameter + 1),   6.7161562765709832e-4 / (type::diameter + 1),
                6.7315699354226843e-4 / (type::diameter + 1),   6.7470502007908783e-4 / (type::diameter + 1),   6.7625978436479298e-4 / (type::diameter + 1),   6.7782136451267269e-4 / (type::diameter + 1),   6.7938983967258432e-4 / (type::diameter + 1),   6.8096529005192981e-4 / (type::diameter + 1),   6.8254779693710506e-4 / (type::diameter + 1),   6.8413744271543620e-4 / (type::diameter + 1),
                6.8573431089761705e-4 / (type::diameter + 1),   6.8733848614066221e-4 / (type::diameter + 1),   6.8895005427139114e-4 / (type::diameter + 1),   6.9056910231045848e-4 / (type::diameter + 1),   6.9219571849694696e-4 / (type::diameter + 1),   6.9382999231353943e-4 / (type::diameter + 1),   6.9547201451228710e-4 / (type::diameter + 1),   6.9712187714099188e-4 / (type::diameter + 1),
                6.9877967357022103e-4 / (type::diameter + 1),   7.0044549852097312e-4 / (type::diameter + 1),   7.0211944809301494e-4 / (type::diameter + 1),   7.0380161979390955e-4 / (type::diameter + 1),   7.0549211256875639e-4 / (type::diameter + 1),   7.0719102683066529e-4 / (type::diameter + 1),   7.0889846449198658e-4 / (type::diameter + 1),   7.1061452899632072e-4 / (type::diameter + 1),
                7.1233932535133129e-4 / (type::diameter + 1),   7.1407296016238630e-4 / (type::diameter + 1),   7.1581554166705348e-4 / (type::diameter + 1),   7.1756717977047635e-4 / (type::diameter + 1),   7.1932798608165839e-4 / (type::diameter + 1),   7.2109807395068425e-4 / (type::diameter + 1),   7.2287755850690735e-4 / (type::diameter + 1),   7.2466655669813464e-4 / (type::diameter + 1),
                7.2646518733084047e-4 / (type::diameter + 1),   7.2827357111144234e-4 / (type::diameter + 1),   7.3009183068867285e-4 / (type::diameter + 1),   7.3192009069708336e-4 / (type::diameter + 1),   7.3375847780171602e-4 / (type::diameter + 1),   7.3560712074398243e-4 / (type::diameter + 1),   7.3746615038878849e-4 / (type::diameter + 1),   7.3933569977294656e-4 / (type::diameter + 1),
                7.4121590415491761e-4 / (type::diameter + 1),   7.4310690106592761e-4 / (type::diameter + 1),   7.4500883036250422e-4 / (type::diameter + 1),   7.4692183428048153e-4 / (type::diameter + 1),   7.4884605749052246e-4 / (type::diameter + 1),   7.5078164715521056e-4 / (type::diameter + 1),   7.5272875298776457e-4 / (type::diameter + 1),   7.5468752731243172e-4 / (type::diameter + 1),
                7.5665812512661760e-4 / (type::diameter + 1),   7.5864070416481281e-4 / (type::diameter + 1),   7.6063542496437930e-4 / (type::diameter + 1),   7.6264245093326135e-4 / (type::diameter + 1),   7.6466194841968932e-4 / (type::diameter + 1),   7.6669408678394668e-4 / (type::diameter + 1),   7.6873903847227391e-4 / (type::diameter + 1),   7.7079697909298597e-4 / (type::diameter + 1),
                7.7286808749488301e-4 / (type::diameter + 1),   7.7495254584803757e-4 / (type::diameter + 1),   7.7705053972704483e-4 / (type::diameter + 1),   7.7916225819682629e-4 / (type::diameter + 1),   7.8128789390108100e-4 / (type::diameter + 1),   7.8342764315348249e-4 / (type::diameter + 1),   7.8558170603172397e-4 / (type::diameter + 1),   7.8775028647451846e-4 / (type::diameter + 1),
                7.8993359238166557e-4 / (type::diameter + 1),   7.9213183571730124e-4 / (type::diameter + 1),   7.9434523261645205e-4 / (type::diameter + 1),   7.9657400349502105e-4 / (type::diameter + 1),   7.9881837316333776e-4 / (type::diameter + 1),   8.0107857094341093e-4 / (type::diameter + 1),   8.0335483079002902e-4 / (type::diameter + 1),   8.0564739141585967e-4 / (type::diameter + 1),
                8.0795649642070690e-4 / (type::diameter + 1),   8.1028239442509144e-4 / (type::diameter + 1),   8.1262533920832781e-4 / (type::diameter + 1),   8.1498558985127962e-4 / (type::diameter + 1),   8.1736341088398308e-4 / (type::diameter + 1),   8.1975907243833784e-4 / (type::diameter + 1),   8.2217285040607365e-4 / (type::diameter + 1),   8.2460502660221127e-4 / (type::diameter + 1),
                8.2705588893424686e-4 / (type::diameter + 1),   8.2952573157729987e-4 / (type::diameter + 1),   8.3201485515547643e-4 / (type::diameter + 1),   8.3452356692971260e-4 / (type::diameter + 1),   8.3705218099237482e-4 / (type::diameter + 1),   8.3960101846890889e-4 / (type::diameter + 1),   8.4217040772684339e-4 / (type::diameter + 1),   8.4476068459246895e-4 / (type::diameter + 1),
                8.4737219257553098e-4 / (type::diameter + 1),   8.5000528310229118e-4 / (type::diameter + 1),   8.5266031575733099e-4 / (type::diameter + 1),   8.5533765853449015e-4 / (type::diameter + 1),   8.5803768809735341e-4 / (type::diameter + 1),   8.6076079004972111e-4 / (type::diameter + 1),   8.6350735921652165e-4 / (type::diameter + 1),   8.6627779993564907e-4 / (type::diameter + 1),
                8.6907252636123457e-4 / (type::diameter + 1),   8.7189196277888883e-4 / (type::diameter + 1),   8.7473654393348100e-4 / (type::diameter + 1),   8.7760671537005182e-4 / (type::diameter + 1),   8.8050293378849130e-4 / (type::diameter + 1),   8.8342566741264675e-4 / (type::diameter + 1),   8.8637539637456463e-4 / (type::diameter + 1),   8.8935261311460957e-4 / (type::diameter + 1),
                8.9235782279824666e-4 / (type::diameter + 1),   8.9539154375031837e-4 / (type::diameter + 1),   8.9845430790769613e-4 / (type::diameter + 1),   9.0154666129123793e-4 / (type::diameter + 1),   9.0466916449803881e-4 / (type::diameter + 1),   9.0782239321501962e-4 / (type::diameter + 1),   9.1100693875496260e-4 / (type::diameter + 1),   9.1422340861616943e-4 / (type::diameter + 1),
                9.1747242706698936e-4 / (type::diameter + 1),   9.2075463575654193e-4 / (type::diameter + 1),   9.2407069435304122e-4 / (type::diameter + 1),   9.2742128121121688e-4 / (type::diameter + 1),   9.3080709407042164e-4 / (type::diameter + 1),   9.3422885078511671e-4 / (type::diameter + 1),   9.3768729008953514e-4 / (type::diameter + 1),   9.4118317239844038e-4 / (type::diameter + 1),
                9.4471728064602270e-4 / (type::diameter + 1),   9.4829042116511146e-4 / (type::diameter + 1),   9.5190342460902641e-4 / (type::diameter + 1),   9.5555714691854768e-4 / (type::diameter + 1),   9.5925247033665277e-4 / (type::diameter + 1),   9.6299030447385051e-4 / (type::diameter + 1),   9.6677158742713783e-4 / (type::diameter + 1),   9.7059728695581708e-4 / (type::diameter + 1),
                9.7446840171763979e-4 / (type::diameter + 1),   9.7838596256899019e-4 / (type::diameter + 1),   9.8235103393308888e-4 / (type::diameter + 1),   9.8636471524048647e-4 / (type::diameter + 1),   9.9042814244643054e-4 / (type::diameter + 1),   9.9454248963002922e-4 / (type::diameter + 1),   9.9870897068050347e-4 / (type::diameter + 1),   1.0029288410762209e-3 / (type::diameter + 1),
                1.0072033997626394e-3 / (type::diameter + 1),   1.0115339911357623e-3 / (type::diameter + 1),   1.0159220071382231e-3 / (type::diameter + 1),   1.0203688894756791e-3 / (type::diameter + 1),   1.0248761319618071e-3 / (type::diameter + 1),   1.0294452830008624e-3 / (type::diameter + 1),   1.0340779482174954e-3 / (type::diameter + 1),   1.0387757932443183e-3 / (type::diameter + 1),
                1.0435405466785911e-3 / (type::diameter + 1),   1.0483740032203548e-3 / (type::diameter + 1),   1.0532780270053953e-3 / (type::diameter + 1),   1.0582545551475736e-3 / (type::diameter + 1),   1.0633056015063330e-3 / (type::diameter + 1),   1.0684332606965909e-3 / (type::diameter + 1),   1.0736397123597652e-3 / (type::diameter + 1),   1.0789272257163841e-3 / (type::diameter + 1),
                1.0842981644226092e-3 / (type::diameter + 1),   1.0897549917550730e-3 / (type::diameter + 1),   1.0953002761507356e-3 / (type::diameter + 1),   1.1009366971310083e-3 / (type::diameter + 1),   1.1066670516422219e-3 / (type::diameter + 1),   1.1124942608476599e-3 / (type::diameter + 1),   1.1184213774098701e-3 / (type::diameter + 1),   1.1244515933058683e-3 / (type::diameter + 1),
                1.1305882482221938e-3 / (type::diameter + 1),   1.1368348385816369e-3 / (type::diameter + 1),   1.1431950272588969e-3 / (type::diameter + 1),   1.1496726540485266e-3 / (type::diameter + 1),   1.1562717469553665e-3 / (type::diameter + 1),   1.1629965343853688e-3 / (type::diameter + 1),   1.1698514583233860e-3 / (type::diameter + 1),   1.1768411885942850e-3 / (type::diameter + 1),
                1.1839706383148127e-3 / (type::diameter + 1),   1.1912449806561691e-3 / (type::diameter + 1),   1.1986696670514609e-3 / (type::diameter + 1),   1.2062504469983750e-3 / (type::diameter + 1),   1.2139933896258248e-3 / (type::diameter + 1),   1.2219049072143403e-3 / (type::diameter + 1),   1.2299917808840238e-3 / (type::diameter + 1),   1.2382611886914588e-3 / (type::diameter + 1),
                1.2467207364086440e-3 / (type::diameter + 1),   1.2553784912935126e-3 / (type::diameter + 1),   1.2642430192037355e-3 / (type::diameter + 1),   1.2733234254542783e-3 / (type::diameter + 1),   1.2826293998757912e-3 / (type::diameter + 1),   1.2921712665967871e-3 / (type::diameter + 1),   1.3019600391494466e-3 / (type::diameter + 1),   1.3120074815888701e-3 / (type::diameter + 1),
                1.3223261764212414e-3 / (type::diameter + 1),   1.3329296002607819e-3 / (type::diameter + 1),   1.3438322082823758e-3 / (type::diameter + 1),   1.3550495287110371e-3 / (type::diameter + 1),   1.3665982687967576e-3 / (type::diameter + 1),   1.3784964339709251e-3 / (type::diameter + 1),   1.3907634621773976e-3 / (type::diameter + 1),   1.4034203757286971e-3 / (type::diameter + 1),
                1.4164899534697839e-3 / (type::diameter + 1),   1.4299969265563873e-3 / (type::diameter + 1),   1.4439682017946636e-3 / (type::diameter + 1),   1.4584331172731702e-3 / (type::diameter + 1),   1.4734237359842940e-3 / (type::diameter + 1),   1.4889751843289665e-3 / (type::diameter + 1),   1.5051260438891419e-3 / (type::diameter + 1),   1.5219188067203952e-3 / (type::diameter + 1),
                1.5394004067723418e-3 / (type::diameter + 1),   1.5576228430344137e-3 / (type::diameter + 1),   1.5766439138265789e-3 / (type::diameter + 1),   1.5965280865771343e-3 / (type::diameter + 1),   1.6173475338201635e-3 / (type::diameter + 1),   1.6391833745117888e-3 / (type::diameter + 1),   1.6621271708173437e-3 / (type::diameter + 1),   1.6862827452652720e-3 / (type::diameter + 1),
                1.7117684030348964e-3 / (type::diameter + 1),   1.7387196712271433e-3 / (type::diameter + 1),   1.7672927043216418e-3 / (type::diameter + 1),   1.7976685572190784e-3 / (type::diameter + 1),   1.8300586012336827e-3 / (type::diameter + 1),   1.8647114648344588e-3 / (type::diameter + 1),   1.9019220366704191e-3 / (type::diameter + 1),   1.9420433005143768e-3 / (type::diameter + 1),
                1.9855021247362247e-3 / (type::diameter + 1),   2.0328206778984357e-3 / (type::diameter + 1),   2.0846460175110070e-3 / (type::diameter + 1),   2.1417918347482962e-3 / (type::diameter + 1),   2.2052987685239426e-3 / (type::diameter + 1),   2.2765239685724229e-3 / (type::diameter + 1),   2.3572783938626298e-3 / (type::diameter + 1),   2.4500453280226908e-3 / (type::diameter + 1),
                2.5583440963573005e-3 / (type::diameter + 1),   2.6873694415021333e-3 / (type::diameter + 1),   2.8451946563855382e-3 / (type::diameter + 1),   3.0452425435680443e-3 / (type::diameter + 1),   3.3119907882924757e-3 / (type::diameter + 1),   3.6965304914378448e-3 / (type::diameter + 1),   4.3316108228152995e-3 / (type::diameter + 1),   5.7512137032250773e-3 / (type::diameter + 1),
                5.7512137032250773e-3 / (type::diameter + 1),   4.3316108228152995e-3 / (type::diameter + 1),   3.6965304914378448e-3 / (type::diameter + 1),   3.3119907882924757e-3 / (type::diameter + 1),   3.0452425435680443e-3 / (type::diameter + 1),   2.8451946563855382e-3 / (type::diameter + 1),   2.6873694415021333e-3 / (type::diameter + 1),   2.5583440963573005e-3 / (type::diameter + 1),
                2.4500453280226908e-3 / (type::diameter + 1),   2.3572783938626298e-3 / (type::diameter + 1),   2.2765239685724229e-3 / (type::diameter + 1),   2.2052987685239426e-3 / (type::diameter + 1),   2.1417918347482962e-3 / (type::diameter + 1),   2.0846460175110070e-3 / (type::diameter + 1),   2.0328206778984357e-3 / (type::diameter + 1),   1.9855021247362247e-3 / (type::diameter + 1),
                1.9420433005143768e-3 / (type::diameter + 1),   1.9019220366704191e-3 / (type::diameter + 1),   1.8647114648344588e-3 / (type::diameter + 1),   1.8300586012336827e-3 / (type::diameter + 1),   1.7976685572190784e-3 / (type::diameter + 1),   1.7672927043216418e-3 / (type::diameter + 1),   1.7387196712271433e-3 / (type::diameter + 1),   1.7117684030348964e-3 / (type::diameter + 1),
                1.6862827452652720e-3 / (type::diameter + 1),   1.6621271708173437e-3 / (type::diameter + 1),   1.6391833745117888e-3 / (type::diameter + 1),   1.6173475338201635e-3 / (type::diameter + 1),   1.5965280865771343e-3 / (type::diameter + 1),   1.5766439138265789e-3 / (type::diameter + 1),   1.5576228430344137e-3 / (type::diameter + 1),   1.5394004067723418e-3 / (type::diameter + 1),
                1.5219188067203952e-3 / (type::diameter + 1),   1.5051260438891419e-3 / (type::diameter + 1),   1.4889751843289665e-3 / (type::diameter + 1),   1.4734237359842940e-3 / (type::diameter + 1),   1.4584331172731702e-3 / (type::diameter + 1),   1.4439682017946636e-3 / (type::diameter + 1),   1.4299969265563873e-3 / (type::diameter + 1),   1.4164899534697839e-3 / (type::diameter + 1),
                1.4034203757286971e-3 / (type::diameter + 1),   1.3907634621773976e-3 / (type::diameter + 1),   1.3784964339709251e-3 / (type::diameter + 1),   1.3665982687967576e-3 / (type::diameter + 1),   1.3550495287110371e-3 / (type::diameter + 1),   1.3438322082823758e-3 / (type::diameter + 1),   1.3329296002607819e-3 / (type::diameter + 1),   1.3223261764212414e-3 / (type::diameter + 1),
                1.3120074815888701e-3 / (type::diameter + 1),   1.3019600391494466e-3 / (type::diameter + 1),   1.2921712665967871e-3 / (type::diameter + 1),   1.2826293998757912e-3 / (type::diameter + 1),   1.2733234254542783e-3 / (type::diameter + 1),   1.2642430192037355e-3 / (type::diameter + 1),   1.2553784912935126e-3 / (type::diameter + 1),   1.2467207364086440e-3 / (type::diameter + 1),
                1.2382611886914588e-3 / (type::diameter + 1),   1.2299917808840238e-3 / (type::diameter + 1),   1.2219049072143403e-3 / (type::diameter + 1),   1.2139933896258248e-3 / (type::diameter + 1),   1.2062504469983750e-3 / (type::diameter + 1),   1.1986696670514609e-3 / (type::diameter + 1),   1.1912449806561691e-3 / (type::diameter + 1),   1.1839706383148127e-3 / (type::diameter + 1),
                1.1768411885942850e-3 / (type::diameter + 1),   1.1698514583233860e-3 / (type::diameter + 1),   1.1629965343853688e-3 / (type::diameter + 1),   1.1562717469553665e-3 / (type::diameter + 1),   1.1496726540485266e-3 / (type::diameter + 1),   1.1431950272588969e-3 / (type::diameter + 1),   1.1368348385816369e-3 / (type::diameter + 1),   1.1305882482221938e-3 / (type::diameter + 1),
                1.1244515933058683e-3 / (type::diameter + 1),   1.1184213774098701e-3 / (type::diameter + 1),   1.1124942608476599e-3 / (type::diameter + 1),   1.1066670516422219e-3 / (type::diameter + 1),   1.1009366971310083e-3 / (type::diameter + 1),   1.0953002761507356e-3 / (type::diameter + 1),   1.0897549917550730e-3 / (type::diameter + 1),   1.0842981644226092e-3 / (type::diameter + 1),
                1.0789272257163841e-3 / (type::diameter + 1),   1.0736397123597652e-3 / (type::diameter + 1),   1.0684332606965909e-3 / (type::diameter + 1),   1.0633056015063330e-3 / (type::diameter + 1),   1.0582545551475736e-3 / (type::diameter + 1),   1.0532780270053953e-3 / (type::diameter + 1),   1.0483740032203548e-3 / (type::diameter + 1),   1.0435405466785911e-3 / (type::diameter + 1),
                1.0387757932443183e-3 / (type::diameter + 1),   1.0340779482174954e-3 / (type::diameter + 1),   1.0294452830008624e-3 / (type::diameter + 1),   1.0248761319618071e-3 / (type::diameter + 1),   1.0203688894756791e-3 / (type::diameter + 1),   1.0159220071382231e-3 / (type::diameter + 1),   1.0115339911357623e-3 / (type::diameter + 1),   1.0072033997626394e-3 / (type::diameter + 1),
                1.0029288410762209e-3 / (type::diameter + 1),   9.9870897068050347e-4 / (type::diameter + 1),   9.9454248963002922e-4 / (type::diameter + 1),   9.9042814244643054e-4 / (type::diameter + 1),   9.8636471524048647e-4 / (type::diameter + 1),   9.8235103393308888e-4 / (type::diameter + 1),   9.7838596256899019e-4 / (type::diameter + 1),   9.7446840171763979e-4 / (type::diameter + 1),
                9.7059728695581708e-4 / (type::diameter + 1),   9.6677158742713783e-4 / (type::diameter + 1),   9.6299030447385051e-4 / (type::diameter + 1),   9.5925247033665277e-4 / (type::diameter + 1),   9.5555714691854768e-4 / (type::diameter + 1),   9.5190342460902641e-4 / (type::diameter + 1),   9.4829042116511146e-4 / (type::diameter + 1),   9.4471728064602270e-4 / (type::diameter + 1),
                9.4118317239844038e-4 / (type::diameter + 1),   9.3768729008953514e-4 / (type::diameter + 1),   9.3422885078511671e-4 / (type::diameter + 1),   9.3080709407042164e-4 / (type::diameter + 1),   9.2742128121121688e-4 / (type::diameter + 1),   9.2407069435304122e-4 / (type::diameter + 1),   9.2075463575654193e-4 / (type::diameter + 1),   9.1747242706698936e-4 / (type::diameter + 1),
                9.1422340861616943e-4 / (type::diameter + 1),   9.1100693875496260e-4 / (type::diameter + 1),   9.0782239321501962e-4 / (type::diameter + 1),   9.0466916449803881e-4 / (type::diameter + 1),   9.0154666129123793e-4 / (type::diameter + 1),   8.9845430790769613e-4 / (type::diameter + 1),   8.9539154375031837e-4 / (type::diameter + 1),   8.9235782279824666e-4 / (type::diameter + 1),
                8.8935261311460957e-4 / (type::diameter + 1),   8.8637539637456463e-4 / (type::diameter + 1),   8.8342566741264675e-4 / (type::diameter + 1),   8.8050293378849130e-4 / (type::diameter + 1),   8.7760671537005182e-4 / (type::diameter + 1),   8.7473654393348100e-4 / (type::diameter + 1),   8.7189196277888883e-4 / (type::diameter + 1),   8.6907252636123457e-4 / (type::diameter + 1),
                8.6627779993564907e-4 / (type::diameter + 1),   8.6350735921652165e-4 / (type::diameter + 1),   8.6076079004972111e-4 / (type::diameter + 1),   8.5803768809735341e-4 / (type::diameter + 1),   8.5533765853449015e-4 / (type::diameter + 1),   8.5266031575733099e-4 / (type::diameter + 1),   8.5000528310229118e-4 / (type::diameter + 1),   8.4737219257553098e-4 / (type::diameter + 1),
                8.4476068459246895e-4 / (type::diameter + 1),   8.4217040772684339e-4 / (type::diameter + 1),   8.3960101846890889e-4 / (type::diameter + 1),   8.3705218099237482e-4 / (type::diameter + 1),   8.3452356692971260e-4 / (type::diameter + 1),   8.3201485515547643e-4 / (type::diameter + 1),   8.2952573157729987e-4 / (type::diameter + 1),   8.2705588893424686e-4 / (type::diameter + 1),
                8.2460502660221127e-4 / (type::diameter + 1),   8.2217285040607365e-4 / (type::diameter + 1),   8.1975907243833784e-4 / (type::diameter + 1),   8.1736341088398308e-4 / (type::diameter + 1),   8.1498558985127962e-4 / (type::diameter + 1),   8.1262533920832781e-4 / (type::diameter + 1),   8.1028239442509144e-4 / (type::diameter + 1),   8.0795649642070690e-4 / (type::diameter + 1),
                8.0564739141585967e-4 / (type::diameter + 1),   8.0335483079002902e-4 / (type::diameter + 1),   8.0107857094341093e-4 / (type::diameter + 1),   7.9881837316333776e-4 / (type::diameter + 1),   7.9657400349502105e-4 / (type::diameter + 1),   7.9434523261645205e-4 / (type::diameter + 1),   7.9213183571730124e-4 / (type::diameter + 1),   7.8993359238166557e-4 / (type::diameter + 1),
                7.8775028647451846e-4 / (type::diameter + 1),   7.8558170603172397e-4 / (type::diameter + 1),   7.8342764315348249e-4 / (type::diameter + 1),   7.8128789390108100e-4 / (type::diameter + 1),   7.7916225819682629e-4 / (type::diameter + 1),   7.7705053972704483e-4 / (type::diameter + 1),   7.7495254584803757e-4 / (type::diameter + 1),   7.7286808749488301e-4 / (type::diameter + 1),
                7.7079697909298597e-4 / (type::diameter + 1),   7.6873903847227391e-4 / (type::diameter + 1),   7.6669408678394668e-4 / (type::diameter + 1),   7.6466194841968932e-4 / (type::diameter + 1),   7.6264245093326135e-4 / (type::diameter + 1),   7.6063542496437930e-4 / (type::diameter + 1),   7.5864070416481281e-4 / (type::diameter + 1),   7.5665812512661760e-4 / (type::diameter + 1),
                7.5468752731243172e-4 / (type::diameter + 1),   7.5272875298776457e-4 / (type::diameter + 1),   7.5078164715521056e-4 / (type::diameter + 1),   7.4884605749052246e-4 / (type::diameter + 1),   7.4692183428048153e-4 / (type::diameter + 1),   7.4500883036250422e-4 / (type::diameter + 1),   7.4310690106592761e-4 / (type::diameter + 1),   7.4121590415491761e-4 / (type::diameter + 1),
                7.3933569977294656e-4 / (type::diameter + 1),   7.3746615038878849e-4 / (type::diameter + 1),   7.3560712074398243e-4 / (type::diameter + 1),   7.3375847780171602e-4 / (type::diameter + 1),   7.3192009069708336e-4 / (type::diameter + 1),   7.3009183068867285e-4 / (type::diameter + 1),   7.2827357111144234e-4 / (type::diameter + 1),   7.2646518733084047e-4 / (type::diameter + 1),
                7.2466655669813464e-4 / (type::diameter + 1),   7.2287755850690735e-4 / (type::diameter + 1),   7.2109807395068425e-4 / (type::diameter + 1),   7.1932798608165839e-4 / (type::diameter + 1),   7.1756717977047635e-4 / (type::diameter + 1),   7.1581554166705348e-4 / (type::diameter + 1),   7.1407296016238630e-4 / (type::diameter + 1),   7.1233932535133129e-4 / (type::diameter + 1),
                7.1061452899632072e-4 / (type::diameter + 1),   7.0889846449198658e-4 / (type::diameter + 1),   7.0719102683066529e-4 / (type::diameter + 1),   7.0549211256875639e-4 / (type::diameter + 1),   7.0380161979390955e-4 / (type::diameter + 1),   7.0211944809301494e-4 / (type::diameter + 1),   7.0044549852097312e-4 / (type::diameter + 1),   6.9877967357022103e-4 / (type::diameter + 1),
                6.9712187714099188e-4 / (type::diameter + 1),   6.9547201451228710e-4 / (type::diameter + 1),   6.9382999231353943e-4 / (type::diameter + 1),   6.9219571849694696e-4 / (type::diameter + 1),   6.9056910231045848e-4 / (type::diameter + 1),   6.8895005427139114e-4 / (type::diameter + 1),   6.8733848614066221e-4 / (type::diameter + 1),   6.8573431089761705e-4 / (type::diameter + 1),
                6.8413744271543620e-4 / (type::diameter + 1),   6.8254779693710506e-4 / (type::diameter + 1),   6.8096529005192981e-4 / (type::diameter + 1),   6.7938983967258432e-4 / (type::diameter + 1),   6.7782136451267269e-4 / (type::diameter + 1),   6.7625978436479298e-4 / (type::diameter + 1),   6.7470502007908783e-4 / (type::diameter + 1),   6.7315699354226843e-4 / (type::diameter + 1),
                6.7161562765709832e-4 / (type::diameter + 1),   6.7008084632232438e-4 / (type::diameter + 1),   6.6855257441304227e-4 / (type::diameter + 1),   6.6703073776148440e-4 / (type::diameter + 1),   6.6551526313821857e-4 / (type::diameter + 1),   6.6400607823374590e-4 / (type::diameter + 1),   6.6250311164048702e-4 / (type::diameter + 1),   6.6100629283514575e-4 / (type::diameter + 1),
                6.5951555216143991e-4 / (type::diameter + 1),   6.5803082081318906e-4 / (type::diameter + 1),   6.5655203081774944e-4 / (type::diameter + 1),   6.5507911501978651e-4 / (type::diameter + 1),   6.5361200706537587e-4 / (type::diameter + 1),   6.5215064138642356e-4 / (type::diameter + 1),   6.5069495318539696e-4 / (type::diameter + 1),   6.4924487842035780e-4 / (type::diameter + 1),
                6.4780035379028910e-4 / (type::diameter + 1),   6.4636131672070786e-4 / (type::diameter + 1),   6.4492770534955582e-4 / (type::diameter + 1),   6.4349945851336063e-4 / (type::diameter + 1),   6.4207651573366000e-4 / (type::diameter + 1),   6.4065881720368174e-4 / (type::diameter + 1),   6.3924630377527255e-4 / (type::diameter + 1),   6.3783891694606889e-4 / (type::diameter + 1),
                6.3643659884690310e-4 / (type::diameter + 1),   6.3503929222943850e-4 / (type::diameter + 1),   6.3364694045402700e-4 / (type::diameter + 1),   6.3225948747778315e-4 / (type::diameter + 1),   6.3087687784286864e-4 / (type::diameter + 1),   6.2949905666498138e-4 / (type::diameter + 1),   6.2812596962204347e-4 / (type::diameter + 1),   6.2675756294308244e-4 / (type::diameter + 1),
                6.2539378339730049e-4 / (type::diameter + 1),   6.2403457828332623e-4 / (type::diameter + 1),   6.2267989541864385e-4 / (type::diameter + 1),   6.2132968312919466e-4 / (type::diameter + 1),   6.1998389023914601e-4 / (type::diameter + 1),   6.1864246606082280e-4 / (type::diameter + 1),   6.1730536038479682e-4 / (type::diameter + 1),   6.1597252347012929e-4 / (type::diameter + 1),
                6.1464390603476209e-4 / (type::diameter + 1),   6.1331945924605326e-4 / (type::diameter + 1),   6.1199913471145236e-4 / (type::diameter + 1),   6.1068288446931149e-4 / (type::diameter + 1),   6.0937066097982781e-4 / (type::diameter + 1),   6.0806241711611338e-4 / (type::diameter + 1),   6.0675810615538839e-4 / (type::diameter + 1),   6.0545768177029381e-4 / (type::diameter + 1),
                6.0416109802031955e-4 / (type::diameter + 1),   6.0286830934334433e-4 / (type::diameter + 1),   6.0157927054728360e-4 / (type::diameter + 1),   6.0029393680184167e-4 / (type::diameter + 1),   5.9901226363036458e-4 / (type::diameter + 1),   5.9773420690179000e-4 / (type::diameter + 1),   5.9645972282269079e-4 / (type::diameter + 1),   5.9518876792940856e-4 / (type::diameter + 1),
                5.9392129908027399e-4 / (type::diameter + 1),   5.9265727344791041e-4 / (type::diameter + 1),   5.9139664851161732e-4 / (type::diameter + 1),   5.9013938204983056e-4 / (type::diameter + 1),   5.8888543213265591e-4 / (type::diameter + 1),   5.8763475711447272e-4 / (type::diameter + 1),   5.8638731562660458e-4 / (type::diameter + 1),   5.8514306657005369e-4 / (type::diameter + 1),
                5.8390196910829579e-4 / (type::diameter + 1),   5.8266398266013263e-4 / (type::diameter + 1),   5.8142906689259872e-4 / (type::diameter + 1),   5.8019718171391938e-4 / (type::diameter + 1),   5.7896828726651686e-4 / (type::diameter + 1),   5.7774234392006167e-4 / (type::diameter + 1),   5.7651931226456585e-4 / (type::diameter + 1),   5.7529915310351519e-4 / (type::diameter + 1),
                5.7408182744703748e-4 / (type::diameter + 1),   5.7286729650510343e-4 / (type::diameter + 1),   5.7165552168075758e-4 / (type::diameter + 1),   5.7044646456337580e-4 / (type::diameter + 1),   5.6924008692194653e-4 / (type::diameter + 1),   5.6803635069837260e-4 / (type::diameter + 1),   5.6683521800079051e-4 / (type::diameter + 1),   5.6563665109690415e-4 / (type::diameter + 1),
                5.6444061240732972e-4 / (type::diameter + 1),   5.6324706449894880e-4 / (type::diameter + 1),   5.6205597007826628e-4 / (type::diameter + 1),   5.6086729198477013e-4 / (type::diameter + 1),   5.5968099318428951e-4 / (type::diameter + 1),   5.5849703676234821e-4 / (type::diameter + 1),   5.5731538591750988e-4 / (type::diameter + 1),   5.5613600395471194e-4 / (type::diameter + 1),
                5.5495885427858451e-4 / (type::diameter + 1),   5.5378390038675106e-4 / (type::diameter + 1),   5.5261110586310734e-4 / (type::diameter + 1),   5.5144043437107480e-4 / (type::diameter + 1),   5.5027184964682512e-4 / (type::diameter + 1),   5.4910531549247205e-4 / (type::diameter + 1),   5.4794079576922669e-4 / (type::diameter + 1),   5.4677825439051269e-4 / (type::diameter + 1),
                5.4561765531503707e-4 / (type::diameter + 1),   5.4445896253981295e-4 / (type::diameter + 1),   5.4330214009313000e-4 / (type::diameter + 1),   5.4214715202746834e-4 / (type::diameter + 1),   5.4099396241235180e-4 / (type::diameter + 1),   5.3984253532713596e-4 / (type::diameter + 1),   5.3869283485372654e-4 / (type::diameter + 1),   5.3754482506922359e-4 / (type::diameter + 1),
                5.3639847003848653e-4 / (type::diameter + 1),   5.3525373380661542e-4 / (type::diameter + 1),   5.3411058039134321e-4 / (type::diameter + 1),   5.3296897377533393e-4 / (type::diameter + 1),   5.3182887789838142e-4 / (type::diameter + 1),   5.3069025664950325e-4 / (type::diameter + 1),   5.2955307385892391e-4 / (type::diameter + 1),   5.2841729328994176e-4 / (type::diameter + 1),
                5.2728287863067345e-4 / (type::diameter + 1),   5.2614979348566963e-4 / (type::diameter + 1),   5.2501800136739568e-4 / (type::diameter + 1),   5.2388746568757051e-4 / (type::diameter + 1),   5.2275814974835682e-4 / (type::diameter + 1),   5.2163001673339541e-4 / (type::diameter + 1),   5.2050302969867644e-4 / (type::diameter + 1),   5.1937715156323961e-4 / (type::diameter + 1),
                5.1825234509969562e-4 / (type::diameter + 1),   5.1712857292456051e-4 / (type::diameter + 1),   5.1600579748839425e-4 / (type::diameter + 1),   5.1488398106573482e-4 / (type::diameter + 1),   5.1376308574481834e-4 / (type::diameter + 1),   5.1264307341707586e-4 / (type::diameter + 1),   5.1152390576639650e-4 / (type::diameter + 1),   5.1040554425814682e-4 / (type::diameter + 1),
                5.0928795012793528e-4 / (type::diameter + 1),   5.0817108437011072e-4 / (type::diameter + 1),   5.0705490772598294e-4 / (type::diameter + 1),   5.0593938067175309e-4 / (type::diameter + 1),   5.0482446340614116e-4 / (type::diameter + 1),   5.0371011583769701e-4 / (type::diameter + 1),   5.0259629757178118e-4 / (type::diameter + 1),   5.0148296789720071e-4 / (type::diameter + 1),
                5.0037008577248484e-4 / (type::diameter + 1),   4.9925760981178458e-4 / (type::diameter + 1),   4.9814549827037955e-4 / (type::diameter + 1),   4.9703370902977450e-4 / (type::diameter + 1),   4.9592219958236752e-4 / (type::diameter + 1),   4.9481092701567046e-4 / (type::diameter + 1),   4.9369984799606189e-4 / (type::diameter + 1),   4.9258891875205132e-4 / (type::diameter + 1),
                4.9147809505703283e-4 / (type::diameter + 1),   4.9036733221150491e-4 / (type::diameter + 1),   4.8925658502473245e-4 / (type::diameter + 1),   4.8814580779582513e-4 / (type::diameter + 1),   4.8703495429420585e-4 / (type::diameter + 1),   4.8592397773944079e-4 / (type::diameter + 1),   4.8481283078040182e-4 / (type::diameter + 1),   4.8370146547373007e-4 / (type::diameter + 1),
                4.8258983326156804e-4 / (type::diameter + 1),   4.8147788494852587e-4 / (type::diameter + 1),   4.8036557067784553e-4 / (type::diameter + 1),   4.7925283990672479e-4 / (type::diameter + 1),   4.7813964138076076e-4 / (type::diameter + 1),   4.7702592310747063e-4 / (type::diameter + 1),   4.7591163232884470e-4 / (type::diameter + 1),   4.7479671549288474e-4 / (type::diameter + 1),
                4.7368111822407756e-4 / (type::diameter + 1),   4.7256478529275122e-4 / (type::diameter + 1),   4.7144766058325818e-4 / (type::diameter + 1),   4.7032968706092645e-4 / (type::diameter + 1),   4.6921080673771644e-4 / (type::diameter + 1),   4.6809096063651749e-4 / (type::diameter + 1),   4.6697008875401429e-4 / (type::diameter + 1),   4.6584813002204898e-4 / (type::diameter + 1),
                4.6472502226740063e-4 / (type::diameter + 1),   4.6360070216989856e-4 / (type::diameter + 1),   4.6247510521878130e-4 / (type::diameter + 1),   4.6134816566720715e-4 / (type::diameter + 1),   4.6021981648481672e-4 / (type::diameter + 1),   4.5908998930824123e-4 / (type::diameter + 1),   4.5795861438944383e-4 / (type::diameter + 1),   4.5682562054177381e-4 / (type::diameter + 1),
                4.5569093508360579e-4 / (type::diameter + 1),   4.5455448377942754e-4 / (type::diameter + 1),   4.5341619077823109e-4 / (type::diameter + 1),   4.5227597854905195e-4 / (type::diameter + 1),   4.5113376781349093e-4 / (type::diameter + 1),   4.4998947747504148e-4 / (type::diameter + 1),   4.4884302454503342e-4 / (type::diameter + 1),   4.4769432406499070e-4 / (type::diameter + 1),
                4.4654328902518634e-4 / (type::diameter + 1),   4.4538983027916266e-4 / (type::diameter + 1),   4.4423385645396758e-4 / (type::diameter + 1),   4.4307527385584019e-4 / (type::diameter + 1),   4.4191398637105876e-4 / (type::diameter + 1),   4.4074989536164313e-4 / (type::diameter + 1),   4.3958289955558005e-4 / (type::diameter + 1),   4.3841289493121502e-4 / (type::diameter + 1),
                4.3723977459542654e-4 / (type::diameter + 1),   4.3606342865516862e-4 / (type::diameter + 1),   4.3488374408193496e-4 / (type::diameter + 1),   4.3370060456866239e-4 / (type::diameter + 1),   4.3251389037855221e-4 / (type::diameter + 1),   4.3132347818524530e-4 / (type::diameter + 1),   4.3012924090374053e-4 / (type::diameter + 1),   4.2893104751139428e-4 / (type::diameter + 1),
                4.2772876285828307e-4 / (type::diameter + 1),   4.2652224746614948e-4 / (type::diameter + 1),   4.2531135731508343e-4 / (type::diameter + 1),   4.2409594361701633e-4 / (type::diameter + 1),   4.2287585257502291e-4 / (type::diameter + 1),   4.2165092512733465e-4 / (type::diameter + 1),   4.2042099667486779e-4 / (type::diameter + 1),   4.1918589679095784e-4 / (type::diameter + 1),
                4.1794544891186846e-4 / (type::diameter + 1),   4.1669947000650592e-4 / (type::diameter + 1),   4.1544777022361763e-4 / (type::diameter + 1),   4.1419015251458370e-4 / (type::diameter + 1),   4.1292641222972120e-4 / (type::diameter + 1),   4.1165633668580967e-4 / (type::diameter + 1),   4.1037970470231012e-4 / (type::diameter + 1),   4.0909628610348510e-4 / (type::diameter + 1),
                4.0780584118333054e-4 / (type::diameter + 1),   4.0650812012989623e-4 / (type::diameter + 1),   4.0520286240519585e-4 / (type::diameter + 1),   4.0388979607648341e-4 / (type::diameter + 1),   4.0256863709419375e-4 / (type::diameter + 1),   4.0123908851130159e-4 / (type::diameter + 1),   3.9990083963823777e-4 / (type::diameter + 1),   3.9855356512680048e-4 / (type::diameter + 1),
                3.9719692397570074e-4 / (type::diameter + 1),   3.9583055844946910e-4 / (type::diameter + 1),   3.9445409290140627e-4 / (type::diameter + 1),   3.9306713249006123e-4 / (type::diameter + 1),   3.9166926177734152e-4 / (type::diameter + 1),   3.9026004319476904e-4 / (type::diameter + 1),   3.8883901536255420e-4 / (type::diameter + 1),   3.8740569124402679e-4 / (type::diameter + 1),
                3.8595955611547845e-4 / (type::diameter + 1),   3.8450006532857422e-4 / (type::diameter + 1),   3.8302664183909911e-4 / (type::diameter + 1),   3.8153867347182342e-4 / (type::diameter + 1),   3.8003550988657773e-4 / (type::diameter + 1),   3.7851645920507957e-4 / (type::diameter + 1),   3.7698078425146797e-4 / (type::diameter + 1),   3.7542769835165452e-4 / (type::diameter + 1),
                3.7385636062721188e-4 / (type::diameter + 1),   3.7226587070824085e-4 / (type::diameter + 1),   3.7065526277604515e-4 / (type::diameter + 1),   3.6902349882993822e-4 / (type::diameter + 1),   3.6736946105239587e-4 / (type::diameter + 1),   3.6569194312213691e-4 / (type::diameter + 1),   3.6398964029438007e-4 / (type::diameter + 1),   3.6226113802995295e-4 / (type::diameter + 1),
                3.6050489890810574e-4 / (type::diameter + 1),   3.5871924749915410e-4 / (type::diameter + 1),   3.5690235279890893e-4 / (type::diameter + 1),   3.5505220773250386e-4 / (type::diameter + 1),   3.5316660511428102e-4 / (type::diameter + 1),   3.5124310929405541e-4 / (type::diameter + 1),   3.4927902251620045e-4 / (type::diameter + 1),   3.4727134474960270e-4 / (type::diameter + 1),
                3.4521672538959636e-4 / (type::diameter + 1),   3.4311140475307431e-4 / (type::diameter + 1),   3.4095114263503813e-4 / (type::diameter + 1),   3.3873113029505674e-4 / (type::diameter + 1),   3.3644588098471659e-4 / (type::diameter + 1),   3.3408909234310643e-4 / (type::diameter + 1),   3.3165347141351495e-4 / (type::diameter + 1),   3.2913050925229932e-4 / (type::diameter + 1),
                3.2651018642881690e-4 / (type::diameter + 1),   3.2378058201430321e-4 / (type::diameter + 1),   3.2092734496718371e-4 / (type::diameter + 1),   3.1793296465583298e-4 / (type::diameter + 1),   3.1477574018092589e-4 / (type::diameter + 1),   3.1142828377047018e-4 / (type::diameter + 1),   3.0785527673641671e-4 / (type::diameter + 1),   3.0400997353862756e-4 / (type::diameter + 1),
                2.9982849700430920e-4 / (type::diameter + 1),   2.9521997798004228e-4 / (type::diameter + 1),   2.9004821488805630e-4 / (type::diameter + 1),   2.8409407716140791e-4 / (type::diameter + 1),   2.7696721223106476e-4 / (type::diameter + 1),   2.6785105422457909e-4 / (type::diameter + 1),   2.5443827317688897e-4 / (type::diameter + 1),   2.3923402393103877e-4 / (type::diameter + 1)
            };
            
            // Density at the proper x-endpoints of the boxes, tail boxes treated specially: { 0, f(x_1), f(x_2), ..., f(x_{n - 2}), 0 }.
            const result_type  m_bottom[n_boxes] = {
                0,                       2.3923402393103877e-4,   4.9367229710792774e-4,   7.6152335133250684e-4,   1.0384905635635716e-3,   1.3225846407249795e-3,   1.6126328556130358e-3,   1.9078528335930781e-3,
                2.2076813305973873e-3,   2.5116913041360149e-3,   2.8195465808724316e-3,   3.1309748646429017e-3,   3.4457506048238276e-3,   3.7636835694796606e-3,   4.0846109144468443e-3,   4.4083914964611475e-3,
                4.7349016828899644e-3,   5.0640321921422638e-3,   5.3956856635557787e-3,   5.7297747558988852e-3,   6.0662206368836017e-3,   6.4049517671786585e-3,   6.7459029098136966e-3,   7.0890143145667709e-3,
                7.4342310399563673e-3,   7.7815023847059700e-3,   8.1307814072221704e-3,   8.4820245165162258e-3,   8.8351911216305069e-3,   9.1902433293630107e-3,   9.5471456821619197e-3,   9.9058649296610738e-3,
                1.0266369828569179e-2,   1.0628630966599132e-2,   1.0992620606893513e-2,   1.1358312550015649e-2,   1.1725682011068045e-2,   1.2094705509897984e-2,   1.2465360772674029e-2,   1.2837626643382270e-2,
                1.3211483004009481e-2,   1.3586910702361136e-2,   1.3963891486612604e-2,   1.4342407945817683e-2,   1.4722443455704261e-2,   1.5103982129176085e-2,   1.5487008771015184e-2,   1.5871508836343758e-2,
                1.6257468392459236e-2,   1.6644874083703263e-2,   1.7033713099065817e-2,   1.7423973142260586e-2,   1.7815642404037928e-2,   1.8208709536527989e-2,   1.8603163629429395e-2,   1.8998994187878865e-2,
                1.9396191111854565e-2,   1.9794744676981366e-2,   2.0194645516619604e-2,   2.0595884605130905e-2,   2.0998453242225099e-2,   2.1402343038301582e-2,   2.1807545900706778e-2,   2.2214054020836674e-2,
                2.2621859862020005e-2,   2.3030956148123490e-2,   2.3441335852825800e-2,   2.3852992189511610e-2,   2.4265918601741331e-2,   2.4680108754255915e-2,   2.5095556524479532e-2,   2.5512255994486038e-2,
                2.5930201443397907e-2,   2.6349387340188865e-2,   2.6769808336863732e-2,   2.7191459261991067e-2,   2.7614335114566090e-2,   2.8038431058183106e-2,   2.8463742415498190e-2,   2.8890264662964339e-2,
                2.9317993425822622e-2,   2.9746924473334016e-2,   3.0177053714237757e-2,   3.0608377192423002e-2,   3.1040891082801555e-2,   3.1474591687370217e-2,   3.1909475431452152e-2,   3.2345538860107320e-2,
                3.2782778634702747e-2,   3.3221191529633962e-2,   3.3660774429189542e-2,   3.4101524324551185e-2,   3.4543438310922244e-2,   3.4986513584778084e-2,   3.5430747441232052e-2,   3.5876137271511214e-2,
                3.6322680560536401e-2,   3.6770374884601391e-2,   3.7219217909146425e-2,   3.7669207386621466e-2,   3.8120341154434957e-2,   3.8572617132984009e-2,   3.9026033323762240e-2,   3.9480587807541668e-2,
                3.9936278742625274e-2,   4.0393104363167047e-2,   4.0851062977556491e-2,   4.1310152966864733e-2,   4.1770372783349549e-2,   4.2231720949016756e-2,   4.2694196054235538e-2,   4.3157796756405436e-2,
                4.3622521778672837e-2,   4.4088369908694886e-2,   4.4555339997448900e-2,   4.5023430958085418e-2,   4.5492641764823134e-2,   4.5962971451884061e-2,   4.6434419112467319e-2,   4.6906983897760070e-2,
                4.7380665015984148e-2,   4.7855461731477032e-2,   4.8331373363805877e-2,   4.8808399286913348e-2,   4.9286538928294108e-2,   4.9765791768200833e-2,   5.0246157338878679e-2,   5.0727635223827205e-2,
                5.1210225057088773e-2,   5.1693926522562503e-2,   5.2178739353342904e-2,   5.2664663331082345e-2,   5.3151698285376551e-2,   5.3639844093172376e-2,   5.4129100678197109e-2,   5.4619468010408614e-2,
                5.5110946105465646e-2,   5.5603535024217698e-2,   5.6097234872213760e-2,   5.6592045799229430e-2,   5.7087967998811798e-2,   5.7585001707841572e-2,   5.8083147206111952e-2,   5.8582404815923736e-2,
                5.9082774901696221e-2,   5.9584257869593422e-2,   6.0086854167165203e-2,   6.0590564283002900e-2,   6.1095388746409041e-2,   6.1601328127080794e-2,   6.2108383034806777e-2,   6.2616554119176888e-2,
                6.3125842069304823e-2,   6.3636247613562970e-2,   6.4147771519329366e-2,   6.4660414592746442e-2,   6.5174177678491261e-2,   6.5689061659556996e-2,   6.6205067457045390e-2,   6.6722196029969950e-2,
                6.7240448375069646e-2,   6.7759825526632886e-2,   6.8280328556331562e-2,   6.8801958573064957e-2,   6.9324716722813314e-2,   6.9848604188500885e-2,   7.0373622189868280e-2,   7.0899771983353950e-2,
                7.1427054861984623e-2,   7.1955472155274565e-2,   7.2485025229133489e-2,   7.3015715485782992e-2,   7.3547544363681374e-2,   7.4080513337456708e-2,   7.4614623917848051e-2,   7.5149877651654666e-2,
                7.5686276121693153e-2,   7.6223820946762376e-2,   7.6762513781616103e-2,   7.7302356316943239e-2,   7.7843350279355591e-2,   7.8385497431383059e-2,   7.8928799571476189e-2,   7.9473258534016002e-2,
                8.0018876189331039e-2,   8.0565654443721552e-2,   8.1113595239490778e-2,   8.1662700554983251e-2,   8.2212972404630076e-2,   8.2764412839001150e-2,   8.3317023944864258e-2,   8.3870807845251009e-2,
                8.4425766699529593e-2,   8.4981902703484305e-2,   8.5539218089401815e-2,   8.6097715126164163e-2,   8.6657396119348453e-2,   8.7218263411333223e-2,   8.7780319381411489e-2,   8.8343566445910438e-2,
                8.8908007058317768e-2,   8.9473643709414672e-2,   9.0040478927415463e-2,   9.0608515278113835e-2,   9.1177755365035782e-2,   9.1748201829599157e-2,   9.2319857351279915e-2,   9.2892724647785018e-2,
                9.3466806475232056e-2,   9.4042105628335571e-2,   9.4618624940600137e-2,   9.5196367284520199e-2,   9.5775335571786716e-2,   9.6355532753500635e-2,   9.6936961820393234e-2,   9.7519625803053366e-2,
                9.8103527772161662e-2,   9.8688670838731716e-2,   9.9275058154358320e-2,   9.9862692911472793e-2,   1.0045157834360545e-1,   1.0104171772565528e-1,   1.0163311437416690e-1,   1.0222577164761481e-1,
                1.0281969294669508e-1,   1.0341488171462449e-1,   1.0401134143744718e-1,   1.0460907564434897e-1,   1.0520808790797934e-1,   1.0580838184478118e-1,   1.0640996111532846e-1,   1.0701282942467180e-1,
                1.0761699052269212e-1,   1.0822244820446242e-1,   1.0882920631061781e-1,   1.0943726872773392e-1,   1.1004663938871375e-1,   1.1065732227318306e-1,   1.1126932140789451e-1,   1.1188264086714056e-1,
                1.1249728477317533e-1,   1.1311325729664546e-1,   1.1373056265703025e-1,   1.1434920512309108e-1,   1.1496918901333022e-1,   1.1559051869645942e-1,   1.1621319859187806e-1,   1.1683723317016139e-1,
                1.1746262695355869e-1,   1.1808938451650177e-1,   1.1871751048612381e-1,   1.1934700954278879e-1,   1.1997788642063166e-1,   1.2061014590810945e-1,   1.2124379284856347e-1,   1.2187883214079291e-1,
                1.2251526873963981e-1,   1.2315310765658588e-1,   1.2379235396036116e-1,   1.2443301277756484e-1,   1.2507508929329850e-1,   1.2571858875181186e-1,   1.2636351645716141e-1,   1.2700987777388212e-1,
                1.2765767812767241e-1,   1.2830692300609277e-1,   1.2895761795927817e-1,   1.2960976860066459e-1,   1.3026338060772997e-1,   1.3091845972274975e-1,   1.3157501175356750e-1,   1.3223304257438069e-1,
                1.3289255812654213e-1,   1.3355356441937728e-1,   1.3421606753101776e-1,   1.3488007360925151e-1,   1.3554558887238973e-1,   1.3621261961015121e-1,   1.3688117218456425e-1,   1.3755125303088658e-1,
                1.3822286865854368e-1,   1.3889602565208595e-1,   1.3957073067216503e-1,   1.4024699045652983e-1,   1.4092481182104250e-1,   1.4160420166071508e-1,   1.4228516695076701e-1,   1.4296771474770412e-1,
                1.4365185219041955e-1,   1.4433758650131717e-1,   1.4502492498745783e-1,   1.4571387504172922e-1,   1.4640444414403968e-1,   1.4709663986253663e-1,   1.4779046985485017e-1,   1.4848594186936246e-1,
                1.4918306374650345e-1,   1.4988184342007367e-1,   1.5058228891859464e-1,   1.5128440836668766e-1,   1.5198820998648157e-1,   1.5269370209905032e-1,   1.5340089312588099e-1,   1.5410979159037298e-1,
                1.5482040611936930e-1,   1.5553274544472063e-1,   1.5624681840488301e-1,   1.5696263394655007e-1,   1.5768020112632054e-1,   1.5839952911240220e-1,   1.5912062718635289e-1,   1.5984350474485979e-1,
                1.6056817130155793e-1,   1.6129463648888877e-1,   1.6202291006000021e-1,   1.6275300189068888e-1,   1.6348492198138597e-1,   1.6421868045918768e-1,   1.6495428757993167e-1,   1.6569175373032045e-1,
                1.6643108943009340e-1,   1.6717230533424832e-1,   1.6791541223531425e-1,   1.6866042106567675e-1,   1.6940734289995723e-1,   1.7015618895744775e-1,   1.7090697060460296e-1,   1.7165969935759073e-1,
                1.7241438688490316e-1,   1.7317104501002978e-1,   1.7392968571419459e-1,   1.7469032113915897e-1,   1.7545296359009223e-1,   1.7621762553851192e-1,   1.7698431962529587e-1,   1.7775305866376814e-1,
                1.7852385564286113e-1,   1.7929672373035601e-1,   1.8007167627620405e-1,   1.8084872681593109e-1,   1.8162788907412792e-1,   1.8240917696802900e-1,   1.8319260461118248e-1,   1.8397818631721421e-1,
                1.8476593660368873e-1,   1.8555587019607039e-1,   1.8634800203178769e-1,   1.8714234726440414e-1,   1.8793892126789917e-1,   1.8873773964106250e-1,   1.8953881821200591e-1,   1.9034217304279594e-1,
                1.9114782043421180e-1,   1.9195577693063251e-1,   1.9276605932505760e-1,   1.9357868466426593e-1,   1.9439367025411721e-1,   1.9521103366500119e-1,   1.9603079273743953e-1,   1.9685296558784560e-1,
                1.9767757061444781e-1,   1.9850462650338206e-1,   1.9933415223495936e-1,   2.0016616709011484e-1,   2.0100069065704455e-1,   2.0183774283803693e-1,   2.0267734385650583e-1,   2.0351951426423268e-1,
                2.0436427494882515e-1,   2.0521164714140068e-1,   2.0606165242450297e-1,   2.0691431274026030e-1,   2.0776965039879479e-1,   2.0862768808689214e-1,   2.0948844887694186e-1,   2.1035195623615839e-1,
                2.1121823403609403e-1,   2.1208730656245527e-1,   2.1295919852523416e-1,   2.1383393506916764e-1,   2.1471154178453769e-1,   2.1559204471832618e-1,   2.1647547038573883e-1,   2.1736184578211339e-1,
                2.1825119839522800e-1,   2.1914355621802625e-1,   2.2003894776177657e-1,   2.2093740206968426e-1,   2.2183894873097550e-1,   2.2274361789547354e-1,   2.2365144028868856e-1,   2.2456244722744352e-1,
                2.2547667063605969e-1,   2.2639414306312668e-1,   2.2731489769888322e-1,   2.2823896839323627e-1,   2.2916638967444748e-1,   2.3009719676851790e-1,   2.3103142561930302e-1,   2.3196911290939256e-1,
                2.3291029608179100e-1,   2.3385501336243702e-1,   2.3480330378360213e-1,   2.3575520720821116e-1,   2.3671076435512970e-1,   2.3767001682546636e-1,   2.3863300712994021e-1,   2.3959977871736735e-1,
                2.4057037600432316e-1,   2.4154484440604080e-1,   2.4252323036860979e-1,   2.4350558140254288e-1,   2.4449194611778337e-1,   2.4548237426022980e-1,   2.4647691674985983e-1,   2.4747562572054033e-1,
                2.4847855456161655e-1,   2.4948575796137919e-1,   2.5049729195251495e-1,   2.5151321395965318e-1,   2.5253358284912886e-1,   2.5355845898109066e-1,   2.5458790426409153e-1,   2.5562198221230902e-1,
                2.5666075800555334e-1,   2.5770429855223193e-1,   2.5875267255545229e-1,   2.5980595058245768e-1,   2.6086420513760525e-1,   2.6192751073911159e-1,   2.6299594399980818e-1,   2.6406958371216794e-1,
                2.6514851093788433e-1,   2.6623280910230694e-1,   2.6732256409406201e-1,   2.6841786437021274e-1,   2.6951880106734375e-1,   2.7062546811898598e-1,   2.7173796237983364e-1,   2.7285638375724351e-1,
                2.7398083535054937e-1,   2.7511142359877157e-1,   2.7624825843735320e-1,   2.7739145346461210e-1,   2.7854112611866063e-1,   2.7969739786561599e-1,   2.8086039440000136e-1,   2.8203024585832475e-1,
                2.8320708704691903e-1,   2.8439105768523385e-1,   2.8558230266589002e-1,   2.8678097233294148e-1,   2.8798722277993985e-1,   2.8920121616956568e-1,   2.9042312107678002e-1,   2.9165311285766404e-1,
                2.9289137404635550e-1,   2.9413809478276414e-1,   2.9539347327405766e-1,   2.9665771629326139e-1,   2.9793103971871567e-1,   2.9921366911859146e-1,   3.0050584038518825e-1,   3.0180780042433769e-1,
                3.0311980790592656e-1,   3.0444213408234781e-1,   3.0577506368260859e-1,   3.0711889589089096e-1,   3.0847394541960200e-1,   3.0984054368839876e-1,   3.1121904012236968e-1,   3.1260980358454708e-1,
                3.1401322396027578e-1,   3.1542971391374556e-1,   3.1685971084030195e-1,   3.1830367904209661e-1,   3.1976211215936978e-1,   3.2123553589535408e-1,   3.2272451107968304e-1,   3.2422963712357219e-1,
                3.2575155593029258e-1,   3.2729095633706492e-1,   3.2884857918009934e-1,   3.3042522309392592e-1,   3.3202175118050305e-1,   3.3363909871432321e-1,   3.3527828208883500e-1,   3.3694040925965235e-1,
                3.3862669200491762e-1,   3.4033846040795251e-1,   3.4207718007917966e-1,   3.4384447278350130e-1,   3.4564214134072038e-1,   3.4747219994195406e-1,   3.4933691140678852e-1,   3.5123883344345894e-1,
                3.5318087674397331e-1,   3.5516637886870954e-1,   3.5719919954660798e-1,   3.5928384556411898e-1,   3.6142563739886728e-1,   3.6363093616739122e-1,   3.6590746013596364e-1,   3.6826473852982627e-1,
                3.7071478385784896e-1,   3.7327312795420626e-1,   3.7596049739570840e-1,   3.7880569205209394e-1,   3.8185093459566198e-1,   3.8516292538395446e-1,   3.8885945587539230e-1,   3.9319106669820760e-1,
                3.9319106669820760e-1,   3.8885945587539230e-1,   3.8516292538395446e-1,   3.8185093459566198e-1,   3.7880569205209394e-1,   3.7596049739570840e-1,   3.7327312795420626e-1,   3.7071478385784896e-1,
                3.6826473852982627e-1,   3.6590746013596364e-1,   3.6363093616739122e-1,   3.6142563739886728e-1,   3.5928384556411898e-1,   3.5719919954660798e-1,   3.5516637886870954e-1,   3.5318087674397331e-1,
                3.5123883344345894e-1,   3.4933691140678852e-1,   3.4747219994195406e-1,   3.4564214134072038e-1,   3.4384447278350130e-1,   3.4207718007917966e-1,   3.4033846040795251e-1,   3.3862669200491762e-1,
                3.3694040925965235e-1,   3.3527828208883500e-1,   3.3363909871432321e-1,   3.3202175118050305e-1,   3.3042522309392592e-1,   3.2884857918009934e-1,   3.2729095633706492e-1,   3.2575155593029258e-1,
                3.2422963712357219e-1,   3.2272451107968304e-1,   3.2123553589535408e-1,   3.1976211215936978e-1,   3.1830367904209661e-1,   3.1685971084030195e-1,   3.1542971391374556e-1,   3.1401322396027578e-1,
                3.1260980358454708e-1,   3.1121904012236968e-1,   3.0984054368839876e-1,   3.0847394541960200e-1,   3.0711889589089096e-1,   3.0577506368260859e-1,   3.0444213408234781e-1,   3.0311980790592656e-1,
                3.0180780042433769e-1,   3.0050584038518825e-1,   2.9921366911859146e-1,   2.9793103971871567e-1,   2.9665771629326139e-1,   2.9539347327405766e-1,   2.9413809478276414e-1,   2.9289137404635550e-1,
                2.9165311285766404e-1,   2.9042312107678002e-1,   2.8920121616956568e-1,   2.8798722277993985e-1,   2.8678097233294148e-1,   2.8558230266589002e-1,   2.8439105768523385e-1,   2.8320708704691903e-1,
                2.8203024585832475e-1,   2.8086039440000136e-1,   2.7969739786561599e-1,   2.7854112611866063e-1,   2.7739145346461210e-1,   2.7624825843735320e-1,   2.7511142359877157e-1,   2.7398083535054937e-1,
                2.7285638375724351e-1,   2.7173796237983364e-1,   2.7062546811898598e-1,   2.6951880106734375e-1,   2.6841786437021274e-1,   2.6732256409406201e-1,   2.6623280910230694e-1,   2.6514851093788433e-1,
                2.6406958371216794e-1,   2.6299594399980818e-1,   2.6192751073911159e-1,   2.6086420513760525e-1,   2.5980595058245768e-1,   2.5875267255545229e-1,   2.5770429855223193e-1,   2.5666075800555334e-1,
                2.5562198221230902e-1,   2.5458790426409153e-1,   2.5355845898109066e-1,   2.5253358284912886e-1,   2.5151321395965318e-1,   2.5049729195251495e-1,   2.4948575796137919e-1,   2.4847855456161655e-1,
                2.4747562572054033e-1,   2.4647691674985983e-1,   2.4548237426022980e-1,   2.4449194611778337e-1,   2.4350558140254288e-1,   2.4252323036860979e-1,   2.4154484440604080e-1,   2.4057037600432316e-1,
                2.3959977871736735e-1,   2.3863300712994021e-1,   2.3767001682546636e-1,   2.3671076435512970e-1,   2.3575520720821116e-1,   2.3480330378360213e-1,   2.3385501336243702e-1,   2.3291029608179100e-1,
                2.3196911290939256e-1,   2.3103142561930302e-1,   2.3009719676851790e-1,   2.2916638967444748e-1,   2.2823896839323627e-1,   2.2731489769888322e-1,   2.2639414306312668e-1,   2.2547667063605969e-1,
                2.2456244722744352e-1,   2.2365144028868856e-1,   2.2274361789547354e-1,   2.2183894873097550e-1,   2.2093740206968426e-1,   2.2003894776177657e-1,   2.1914355621802625e-1,   2.1825119839522800e-1,
                2.1736184578211339e-1,   2.1647547038573883e-1,   2.1559204471832618e-1,   2.1471154178453769e-1,   2.1383393506916764e-1,   2.1295919852523416e-1,   2.1208730656245527e-1,   2.1121823403609403e-1,
                2.1035195623615839e-1,   2.0948844887694186e-1,   2.0862768808689214e-1,   2.0776965039879479e-1,   2.0691431274026030e-1,   2.0606165242450297e-1,   2.0521164714140068e-1,   2.0436427494882515e-1,
                2.0351951426423268e-1,   2.0267734385650583e-1,   2.0183774283803693e-1,   2.0100069065704455e-1,   2.0016616709011484e-1,   1.9933415223495936e-1,   1.9850462650338206e-1,   1.9767757061444781e-1,
                1.9685296558784560e-1,   1.9603079273743953e-1,   1.9521103366500119e-1,   1.9439367025411721e-1,   1.9357868466426593e-1,   1.9276605932505760e-1,   1.9195577693063251e-1,   1.9114782043421180e-1,
                1.9034217304279594e-1,   1.8953881821200591e-1,   1.8873773964106250e-1,   1.8793892126789917e-1,   1.8714234726440414e-1,   1.8634800203178769e-1,   1.8555587019607039e-1,   1.8476593660368873e-1,
                1.8397818631721421e-1,   1.8319260461118248e-1,   1.8240917696802900e-1,   1.8162788907412792e-1,   1.8084872681593109e-1,   1.8007167627620405e-1,   1.7929672373035601e-1,   1.7852385564286113e-1,
                1.7775305866376814e-1,   1.7698431962529587e-1,   1.7621762553851192e-1,   1.7545296359009223e-1,   1.7469032113915897e-1,   1.7392968571419459e-1,   1.7317104501002978e-1,   1.7241438688490316e-1,
                1.7165969935759073e-1,   1.7090697060460296e-1,   1.7015618895744775e-1,   1.6940734289995723e-1,   1.6866042106567675e-1,   1.6791541223531425e-1,   1.6717230533424832e-1,   1.6643108943009340e-1,
                1.6569175373032045e-1,   1.6495428757993167e-1,   1.6421868045918768e-1,   1.6348492198138597e-1,   1.6275300189068888e-1,   1.6202291006000021e-1,   1.6129463648888877e-1,   1.6056817130155793e-1,
                1.5984350474485979e-1,   1.5912062718635289e-1,   1.5839952911240220e-1,   1.5768020112632054e-1,   1.5696263394655007e-1,   1.5624681840488301e-1,   1.5553274544472063e-1,   1.5482040611936930e-1,
                1.5410979159037298e-1,   1.5340089312588099e-1,   1.5269370209905032e-1,   1.5198820998648157e-1,   1.5128440836668766e-1,   1.5058228891859464e-1,   1.4988184342007367e-1,   1.4918306374650345e-1,
                1.4848594186936246e-1,   1.4779046985485017e-1,   1.4709663986253663e-1,   1.4640444414403968e-1,   1.4571387504172922e-1,   1.4502492498745783e-1,   1.4433758650131717e-1,   1.4365185219041955e-1,
                1.4296771474770412e-1,   1.4228516695076701e-1,   1.4160420166071508e-1,   1.4092481182104250e-1,   1.4024699045652983e-1,   1.3957073067216503e-1,   1.3889602565208595e-1,   1.3822286865854368e-1,
                1.3755125303088658e-1,   1.3688117218456425e-1,   1.3621261961015121e-1,   1.3554558887238973e-1,   1.3488007360925151e-1,   1.3421606753101776e-1,   1.3355356441937728e-1,   1.3289255812654213e-1,
                1.3223304257438069e-1,   1.3157501175356750e-1,   1.3091845972274975e-1,   1.3026338060772997e-1,   1.2960976860066459e-1,   1.2895761795927817e-1,   1.2830692300609277e-1,   1.2765767812767241e-1,
                1.2700987777388212e-1,   1.2636351645716141e-1,   1.2571858875181186e-1,   1.2507508929329850e-1,   1.2443301277756484e-1,   1.2379235396036116e-1,   1.2315310765658588e-1,   1.2251526873963981e-1,
                1.2187883214079291e-1,   1.2124379284856347e-1,   1.2061014590810945e-1,   1.1997788642063166e-1,   1.1934700954278879e-1,   1.1871751048612381e-1,   1.1808938451650177e-1,   1.1746262695355869e-1,
                1.1683723317016139e-1,   1.1621319859187806e-1,   1.1559051869645942e-1,   1.1496918901333022e-1,   1.1434920512309108e-1,   1.1373056265703025e-1,   1.1311325729664546e-1,   1.1249728477317533e-1,
                1.1188264086714056e-1,   1.1126932140789451e-1,   1.1065732227318306e-1,   1.1004663938871375e-1,   1.0943726872773392e-1,   1.0882920631061781e-1,   1.0822244820446242e-1,   1.0761699052269212e-1,
                1.0701282942467180e-1,   1.0640996111532846e-1,   1.0580838184478118e-1,   1.0520808790797934e-1,   1.0460907564434897e-1,   1.0401134143744718e-1,   1.0341488171462449e-1,   1.0281969294669508e-1,
                1.0222577164761481e-1,   1.0163311437416690e-1,   1.0104171772565528e-1,   1.0045157834360545e-1,   9.9862692911472793e-2,   9.9275058154358320e-2,   9.8688670838731716e-2,   9.8103527772161662e-2,
                9.7519625803053366e-2,   9.6936961820393234e-2,   9.6355532753500635e-2,   9.5775335571786716e-2,   9.5196367284520199e-2,   9.4618624940600137e-2,   9.4042105628335571e-2,   9.3466806475232056e-2,
                9.2892724647785018e-2,   9.2319857351279915e-2,   9.1748201829599157e-2,   9.1177755365035782e-2,   9.0608515278113835e-2,   9.0040478927415463e-2,   8.9473643709414672e-2,   8.8908007058317768e-2,
                8.8343566445910438e-2,   8.7780319381411489e-2,   8.7218263411333223e-2,   8.6657396119348453e-2,   8.6097715126164163e-2,   8.5539218089401815e-2,   8.4981902703484305e-2,   8.4425766699529593e-2,
                8.3870807845251009e-2,   8.3317023944864258e-2,   8.2764412839001150e-2,   8.2212972404630076e-2,   8.1662700554983251e-2,   8.1113595239490778e-2,   8.0565654443721552e-2,   8.0018876189331039e-2,
                7.9473258534016002e-2,   7.8928799571476189e-2,   7.8385497431383059e-2,   7.7843350279355591e-2,   7.7302356316943239e-2,   7.6762513781616103e-2,   7.6223820946762376e-2,   7.5686276121693153e-2,
                7.5149877651654666e-2,   7.4614623917848051e-2,   7.4080513337456708e-2,   7.3547544363681374e-2,   7.3015715485782992e-2,   7.2485025229133489e-2,   7.1955472155274565e-2,   7.1427054861984623e-2,
                7.0899771983353950e-2,   7.0373622189868280e-2,   6.9848604188500885e-2,   6.9324716722813314e-2,   6.8801958573064957e-2,   6.8280328556331562e-2,   6.7759825526632886e-2,   6.7240448375069646e-2,
                6.6722196029969950e-2,   6.6205067457045390e-2,   6.5689061659556996e-2,   6.5174177678491261e-2,   6.4660414592746442e-2,   6.4147771519329366e-2,   6.3636247613562970e-2,   6.3125842069304823e-2,
                6.2616554119176888e-2,   6.2108383034806777e-2,   6.1601328127080794e-2,   6.1095388746409041e-2,   6.0590564283002900e-2,   6.0086854167165203e-2,   5.9584257869593422e-2,   5.9082774901696221e-2,
                5.8582404815923736e-2,   5.8083147206111952e-2,   5.7585001707841572e-2,   5.7087967998811798e-2,   5.6592045799229430e-2,   5.6097234872213760e-2,   5.5603535024217698e-2,   5.5110946105465646e-2,
                5.4619468010408614e-2,   5.4129100678197109e-2,   5.3639844093172376e-2,   5.3151698285376551e-2,   5.2664663331082345e-2,   5.2178739353342904e-2,   5.1693926522562503e-2,   5.1210225057088773e-2,
                5.0727635223827205e-2,   5.0246157338878679e-2,   4.9765791768200833e-2,   4.9286538928294108e-2,   4.8808399286913348e-2,   4.8331373363805877e-2,   4.7855461731477032e-2,   4.7380665015984148e-2,
                4.6906983897760070e-2,   4.6434419112467319e-2,   4.5962971451884061e-2,   4.5492641764823134e-2,   4.5023430958085418e-2,   4.4555339997448900e-2,   4.4088369908694886e-2,   4.3622521778672837e-2,
                4.3157796756405436e-2,   4.2694196054235538e-2,   4.2231720949016756e-2,   4.1770372783349549e-2,   4.1310152966864733e-2,   4.0851062977556491e-2,   4.0393104363167047e-2,   3.9936278742625274e-2,
                3.9480587807541668e-2,   3.9026033323762240e-2,   3.8572617132984009e-2,   3.8120341154434957e-2,   3.7669207386621466e-2,   3.7219217909146425e-2,   3.6770374884601391e-2,   3.6322680560536401e-2,
                3.5876137271511214e-2,   3.5430747441232052e-2,   3.4986513584778084e-2,   3.4543438310922244e-2,   3.4101524324551185e-2,   3.3660774429189542e-2,   3.3221191529633962e-2,   3.2782778634702747e-2,
                3.2345538860107320e-2,   3.1909475431452152e-2,   3.1474591687370217e-2,   3.1040891082801555e-2,   3.0608377192423002e-2,   3.0177053714237757e-2,   2.9746924473334016e-2,   2.9317993425822622e-2,
                2.8890264662964339e-2,   2.8463742415498190e-2,   2.8038431058183106e-2,   2.7614335114566090e-2,   2.7191459261991067e-2,   2.6769808336863732e-2,   2.6349387340188865e-2,   2.5930201443397907e-2,
                2.5512255994486038e-2,   2.5095556524479532e-2,   2.4680108754255915e-2,   2.4265918601741331e-2,   2.3852992189511610e-2,   2.3441335852825800e-2,   2.3030956148123490e-2,   2.2621859862020005e-2,
                2.2214054020836674e-2,   2.1807545900706778e-2,   2.1402343038301582e-2,   2.0998453242225099e-2,   2.0595884605130905e-2,   2.0194645516619604e-2,   1.9794744676981366e-2,   1.9396191111854565e-2,
                1.8998994187878865e-2,   1.8603163629429395e-2,   1.8208709536527989e-2,   1.7815642404037928e-2,   1.7423973142260586e-2,   1.7033713099065817e-2,   1.6644874083703263e-2,   1.6257468392459236e-2,
                1.5871508836343758e-2,   1.5487008771015184e-2,   1.5103982129176085e-2,   1.4722443455704261e-2,   1.4342407945817683e-2,   1.3963891486612604e-2,   1.3586910702361136e-2,   1.3211483004009481e-2,
                1.2837626643382270e-2,   1.2465360772674029e-2,   1.2094705509897984e-2,   1.1725682011068045e-2,   1.1358312550015649e-2,   1.0992620606893513e-2,   1.0628630966599132e-2,   1.0266369828569179e-2,
                9.9058649296610738e-3,   9.5471456821619197e-3,   9.1902433293630107e-3,   8.8351911216305069e-3,   8.4820245165162258e-3,   8.1307814072221704e-3,   7.7815023847059700e-3,   7.4342310399563673e-3,
                7.0890143145667709e-3,   6.7459029098136966e-3,   6.4049517671786585e-3,   6.0662206368836017e-3,   5.7297747558988852e-3,   5.3956856635557787e-3,   5.0640321921422638e-3,   4.7349016828899644e-3,
                4.4083914964611475e-3,   4.0846109144468443e-3,   3.7636835694796606e-3,   3.4457506048238276e-3,   3.1309748646429017e-3,   2.8195465808724316e-3,   2.5116913041360149e-3,   2.2076813305973873e-3,
                1.9078528335930781e-3,   1.6126328556130358e-3,   1.3225846407249795e-3,   1.0384905635635716e-3,   7.6152335133250684e-4,   4.9367229710792774e-4,   2.3923402393103877e-4,   0
            };
            
            // (<diameter> + 1)-upscaled probability of simple coverage of the boxes: { (x_1 - m) / (x_0* - m), (x_2 - m) / (x_1 - m), ..., (m - x_{n - 1}) / (m - x_n*) }.
            const uniform_type m_coverage_scaled[n_boxes] = {
                static_cast<uniform_type>(9.4024385932190320e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.4992447916055538e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6708578631726145e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7491371519761030e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7947190356283909e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8248166290312643e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8462948295338087e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8624559422953583e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.8750938025635511e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8852703103650386e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8936558322908981e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9006952777506155e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9066960058621081e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9118774501741596e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9164006353256985e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9203865108271144e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9239277625992363e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9270966641709417e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9299504385456507e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9325350076814744e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9348876697457577e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9370390465571714e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9390145238720378e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9408353326276372e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9425193717007546e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9440818417248817e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9455357388730686e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9468922435304656e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9481610291471654e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9493505098231604e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9504680403966768e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9515200793715278e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9525123225202461e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9534498131617767e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9543370337465338e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9551779823564949e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9559762369516694e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9567350096012964e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9574571924815539e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9581453970673523e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9588019876690200e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9594291102469713e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9600287172650914e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9606025892062892e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9611523532636993e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9616794996324382e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9621853957551046e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9626712988158604e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9631383667302269e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9635876678385534e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9640201894788057e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9644368455875651e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9648384834558754e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9652258897480108e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9655997958756795e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9659608828071046e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9663097853793938e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9666470961732801e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9669733690013941e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9672891220544854e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9675948407442543e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9678909802765244e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9681779679842567e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9684562054462619e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9687260704143247e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9689879185687376e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9692420851198797e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9694888862714329e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9697286205590413e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9699615700766610e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9701880016014894e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9704081676271668e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9706223073138968e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9708306473632086e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9710334028242733e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9712307778379689e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9714229663242525e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9716101526178386e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9717925120566807e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9719702115273138e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9721434099707162e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9723122588520010e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9724769025969313e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9726374789979729e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9727941195923467e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9729469500143169e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9730960903237501e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9732416553127951e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9733837547923746e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9735224938600259e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9736579731504993e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9737902890704016e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9739195340180595e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9740457965896855e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9741691617728327e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9742897111280495e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9744075229595670e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9745226724757882e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9746352319402850e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9747452708139542e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9748528558889326e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9749580514148264e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9750609192177645e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9751615188127510e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9752599075097530e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9753561405139293e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9754502710203752e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9755423503037322e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9756324278029834e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9757205512017373e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9758067665042761e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9758911181076289e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9759736488699104e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9760544001751492e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9761334119948152e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9762107229462411e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9762863703481186e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9763603902732408e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9764328175986476e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9765036860533232e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9765730282635838e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9766408757962849e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767072591999700e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767722080440737e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768357509562859e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768979156581769e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9769587289991772e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9770182169889994e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9770764048285854e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771333169396555e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771889769929337e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772434079351160e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772966320146480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773486708063706e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773995452350930e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9774492755981456e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9774978815869631e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775453823077480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775917963012566e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776371415617527e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776814355551679e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777246952365074e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777669370665358e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778081770277789e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9778484306398723e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778877129742869e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779260386684621e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779634219393711e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779998765965463e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780354160545890e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780700533451852e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781038011286512e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9781366717050284e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781686770247489e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781998286988882e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782301380090251e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782596159167249e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782882730726610e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783161198253926e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783431662298100e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9783694220552642e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783948967933919e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784195996656493e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784435396305667e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784667253907349e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784891653995341e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785108678676164e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785318407691501e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9785520918478377e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785716286227128e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785904583937290e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786085882471444e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786260250607125e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786427755086857e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786588460666383e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786742430161162e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9786889724491198e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787030402724247e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787164522117492e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787292138157702e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787413304599964e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787528073505014e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787636495275232e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787738618689339e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9787834490935838e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787924157645252e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788007662921194e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788085049370299e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788156358131076e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788221628901695e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788280899966752e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788334208223049e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9788381589204411e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788423077105574e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788458704805175e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788488503887863e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788512504665572e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788530736197963e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788543226312071e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788550001621178e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9788551087542925e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788546508316703e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788536287020315e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788520445585960e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788499004815529e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788471984395246e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788439402909667e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788401277855057e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9788357625652145e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788308461658291e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788253800179068e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788193654479271e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788128036793369e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788056958335414e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787980429308408e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787898458913156e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9787811055356593e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787718225859617e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787619976664416e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787516313041320e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787407239295158e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787292758771163e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787172873860391e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787047586004699e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9786916895701263e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786780802506654e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786639305040467e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786492400988522e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786340087105627e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786182359217923e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786019212224794e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785850640100363e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9785676635894578e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785497191733867e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785312298821400e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785121947436923e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784926126936199e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784724825750032e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784518031382886e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784305730411102e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9784087908480706e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783864550304809e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783635639660608e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783401159385972e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783161091375624e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782915416576913e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782664114985169e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782407165638655e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9782144546613090e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781876235015762e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781602206979216e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781322437654510e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781036901204052e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780745570793996e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780448418586197e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780145415729727e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9779836532351944e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779521737549097e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779200999376476e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778874284838099e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778541559875914e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778202789358526e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777857937069436e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777506965694778e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9777149836810552e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776786510869341e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776416947186507e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776041103925848e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775658938084711e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775270405478554e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9774875460724934e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9774474057226921e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9774066147155920e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773651681433885e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773230609714922e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772802880366252e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772368440448536e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771927235695531e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771479210493067e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771024307857343e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9770562469412493e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9770093635367431e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9769617744491954e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9769134734092062e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768644539984505e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768147096470509e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767642336308677e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767130190687037e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9766610589194205e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9766083459789656e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9765548728773061e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9765006320752668e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9764456158612707e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9763898163479781e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9763332254688215e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9762758349744335e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9762176364289646e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9761586212062870e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9760987804860809e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9760381052498005e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9759765862765155e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9759142141386231e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9758509791974289e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9757868715985898e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9757218812674161e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9756559979040283e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9755892109783623e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9755215097250206e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9754528831379611e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9753833199650216e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9753128087022717e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9752413375881876e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9751688945976437e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9750954674357142e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9750210435312785e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9749456100304241e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9748691537896382e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9747916613687830e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9747131190238451e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9746335126994512e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9745528280211431e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9744710502874016e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9743881644614108e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9743041551625544e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9742190066576315e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9741327028517847e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9740452272791273e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9739565630930598e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9738666930562626e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9737755995303545e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9736832644652024e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9735896693878697e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9734947953911896e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9733986231219480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9733011327686613e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9732023040489332e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9731021161963728e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9730005479470586e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9728975775255272e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9727931826302708e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9726873404187208e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9725800274916981e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9724712198773077e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9723608930142545e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9722490217345565e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9721355802456293e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9720205421117170e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9719038802346402e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9717855668338326e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9716655734256358e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9715438708018198e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9714204290072956e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9712952173169849e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9711682042118093e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9710393573537600e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9709086435600068e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9707760287760039e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9706414780475464e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9705049554917290e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9703664242667591e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9702258465405681e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9700831834581676e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9699383951076906e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9697914404850556e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9696422774571890e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9694908627237365e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9693371517771904e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9691810988613571e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9690226569280826e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9688617775921514e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9686984110842678e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9685325062020246e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9683640102587572e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9681928690301775e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9680190266986731e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9678424257951532e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9676630071383137e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9674807097711870e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9672954708948349e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9671072257990319e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9669159077897807e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9667214481134877e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9665237758776195e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9663228179676469e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9661184989600743e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9659107410313357e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9656994638623276e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9654845845383332e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9652660174440755e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9650436741536220e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9648174633148423e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9645872905281032e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9643530582188627e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9641146655038019e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9638720080501089e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9636249779275038e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9633734634525635e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9631173490248737e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9628565149545057e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9625908372802750e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9623201875782037e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9620444327595637e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9617634348578347e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9614770508038597e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9611851321884287e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9608875250114619e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9605840694169033e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9602745994123635e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9599589425724804e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9596369197248815e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9593083446175484e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9589730235662821e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9586307550808692e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9582813294684308e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9579245284123131e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9575601245247401e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9571878808713047e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9568075504652024e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9564188757289425e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9560215879210665e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9556154065251913e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9552000385984575e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9547751780761989e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9543405050293625e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9538956848708904e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9534403675069223e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9529741864282898e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9524967577373447e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9520076791046842e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9515065286498120e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9509928637391819e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9504662196944223e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9499261084028115e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9493720168212622e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9488034053641697e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9482197061644678e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9476203211961020e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9470046202448608e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9463719387130804e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9457215752421348e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9450527891348170e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9443647975576823e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9436567725011204e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9429278374723218e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9421770638933475e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9414034671731610e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9406060024186606e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9397835597454060e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9389349591437563e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9380589448504581e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9371541791691922e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9362192356760995e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9352525917376670e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9342526202583953e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9332175805641314e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9321456083135820e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9310347043149685e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9298827221066554e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9286873541393988e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9274461163730224e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9261563310711400e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9248151075431285e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9234193205418630e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9219655859774480e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9204502335497242e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9188692758337063e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9172183732698570e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9154927944121516e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9136873706673773e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9117964446141899e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9098138108139717e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9077326478096646e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9055454397434977e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9032438856969856e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9008187944500897e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8982599618492666e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8955560273378165e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8926943053988840e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8896605866416729e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8864389019579370e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.8830112414981491e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8793572180417060e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8754536614937606e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8712741274977936e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8667882981784826e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8619612463571465e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8567525255432275e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8511150356295900e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.8449935970803999e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8383231423712239e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8310263993022896e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8230108916033097e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8141650102212868e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8043528014371051e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7934069552757601e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7811192258098370e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.7672271161117383e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7513950129794750e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7331868750727354e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7120257142384703e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6871317805929155e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6574251666648381e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6213664575955882e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.5766841196662679e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.5198823684148442e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.4452920311473452e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.3430806107545234e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.1945984702996240e-1 * (type::diameter + 1)),   static_cast<uniform_type>(8.9597280367737636e-1 * (type::diameter + 1)),   static_cast<uniform_type>(8.5338472052189380e-1 * (type::diameter + 1)),   static_cast<uniform_type>(7.5316464425348780e-1 * (type::diameter + 1)),   static_cast<uniform_type>(2.e-48 * (type::diameter + 1)),
                static_cast<uniform_type>(2.e-48 * (type::diameter + 1)),                  static_cast<uniform_type>(7.5316464425348780e-1 * (type::diameter + 1)),   static_cast<uniform_type>(8.5338472052189380e-1 * (type::diameter + 1)),   static_cast<uniform_type>(8.9597280367737636e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.1945984702996240e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.3430806107545234e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.4452920311473452e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.5198823684148442e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.5766841196662679e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6213664575955882e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6574251666648381e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6871317805929155e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7120257142384703e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7331868750727354e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7513950129794750e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7672271161117383e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.7811192258098370e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7934069552757601e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8043528014371051e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8141650102212868e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8230108916033097e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8310263993022896e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8383231423712239e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8449935970803999e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.8511150356295900e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8567525255432275e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8619612463571465e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8667882981784826e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8712741274977936e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8754536614937606e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8793572180417060e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8830112414981491e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.8864389019579370e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8896605866416729e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8926943053988840e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8955560273378165e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8982599618492666e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9008187944500897e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9032438856969856e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9055454397434977e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9077326478096646e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9098138108139717e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9117964446141899e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9136873706673773e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9154927944121516e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9172183732698570e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9188692758337063e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9204502335497242e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9219655859774480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9234193205418630e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9248151075431285e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9261563310711400e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9274461163730224e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9286873541393988e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9298827221066554e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9310347043149685e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9321456083135820e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9332175805641314e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9342526202583953e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9352525917376670e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9362192356760995e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9371541791691922e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9380589448504581e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9389349591437563e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9397835597454060e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9406060024186606e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9414034671731610e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9421770638933475e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9429278374723218e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9436567725011204e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9443647975576823e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9450527891348170e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9457215752421348e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9463719387130804e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9470046202448608e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9476203211961020e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9482197061644678e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9488034053641697e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9493720168212622e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9499261084028115e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9504662196944223e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9509928637391819e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9515065286498120e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9520076791046842e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9524967577373447e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9529741864282898e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9534403675069223e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9538956848708904e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9543405050293625e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9547751780761989e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9552000385984575e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9556154065251913e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9560215879210665e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9564188757289425e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9568075504652024e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9571878808713047e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9575601245247401e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9579245284123131e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9582813294684308e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9586307550808692e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9589730235662821e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9593083446175484e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9596369197248815e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9599589425724804e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9602745994123635e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9605840694169033e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9608875250114619e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9611851321884287e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9614770508038597e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9617634348578347e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9620444327595637e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9623201875782037e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9625908372802750e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9628565149545057e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9631173490248737e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9633734634525635e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9636249779275038e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9638720080501089e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9641146655038019e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9643530582188627e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9645872905281032e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9648174633148423e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9650436741536220e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9652660174440755e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9654845845383332e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9656994638623276e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9659107410313357e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9661184989600743e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9663228179676469e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9665237758776195e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9667214481134877e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9669159077897807e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9671072257990319e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9672954708948349e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9674807097711870e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9676630071383137e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9678424257951532e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9680190266986731e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9681928690301775e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9683640102587572e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9685325062020246e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9686984110842678e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9688617775921514e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9690226569280826e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9691810988613571e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9693371517771904e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9694908627237365e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9696422774571890e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9697914404850556e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9699383951076906e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9700831834581676e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9702258465405681e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9703664242667591e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9705049554917290e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9706414780475464e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9707760287760039e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9709086435600068e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9710393573537600e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9711682042118093e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9712952173169849e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9714204290072956e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9715438708018198e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9716655734256358e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9717855668338326e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9719038802346402e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9720205421117170e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9721355802456293e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9722490217345565e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9723608930142545e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9724712198773077e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9725800274916981e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9726873404187208e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9727931826302708e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9728975775255272e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9730005479470586e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9731021161963728e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9732023040489332e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9733011327686613e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9733986231219480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9734947953911896e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9735896693878697e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9736832644652024e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9737755995303545e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9738666930562626e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9739565630930598e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9740452272791273e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9741327028517847e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9742190066576315e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9743041551625544e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9743881644614108e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9744710502874016e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9745528280211431e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9746335126994512e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9747131190238451e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9747916613687830e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9748691537896382e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9749456100304241e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9750210435312785e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9750954674357142e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9751688945976437e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9752413375881876e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9753128087022717e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9753833199650216e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9754528831379611e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9755215097250206e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9755892109783623e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9756559979040283e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9757218812674161e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9757868715985898e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9758509791974289e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9759142141386231e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9759765862765155e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9760381052498005e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9760987804860809e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9761586212062870e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9762176364289646e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9762758349744335e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9763332254688215e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9763898163479781e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9764456158612707e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9765006320752668e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9765548728773061e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9766083459789656e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9766610589194205e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9767130190687037e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767642336308677e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768147096470509e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768644539984505e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9769134734092062e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9769617744491954e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9770093635367431e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9770562469412493e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9771024307857343e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771479210493067e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771927235695531e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772368440448536e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772802880366252e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773230609714922e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773651681433885e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9774066147155920e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9774474057226921e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9774875460724934e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775270405478554e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775658938084711e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776041103925848e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776416947186507e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776786510869341e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777149836810552e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9777506965694778e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777857937069436e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778202789358526e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778541559875914e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778874284838099e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779200999376476e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779521737549097e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779836532351944e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9780145415729727e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780448418586197e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780745570793996e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781036901204052e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781322437654510e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781602206979216e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781876235015762e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782144546613090e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9782407165638655e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782664114985169e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782915416576913e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783161091375624e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783401159385972e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783635639660608e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783864550304809e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784087908480706e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9784305730411102e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784518031382886e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784724825750032e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784926126936199e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785121947436923e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785312298821400e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785497191733867e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785676635894578e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9785850640100363e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786019212224794e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786182359217923e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786340087105627e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786492400988522e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786639305040467e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786780802506654e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786916895701263e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9787047586004699e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787172873860391e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787292758771163e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787407239295158e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787516313041320e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787619976664416e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787718225859617e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787811055356593e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9787898458913156e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787980429308408e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788056958335414e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788128036793369e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788193654479271e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788253800179068e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788308461658291e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788357625652145e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9788401277855057e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788439402909667e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788471984395246e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788499004815529e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788520445585960e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788536287020315e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788546508316703e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788551087542925e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9788550001621178e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788543226312071e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788530736197963e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788512504665572e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788488503887863e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788458704805175e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788423077105574e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788381589204411e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9788334208223049e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788280899966752e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788221628901695e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788156358131076e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788085049370299e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9788007662921194e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787924157645252e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787834490935838e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9787738618689339e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787636495275232e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787528073505014e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787413304599964e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787292138157702e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787164522117492e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9787030402724247e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786889724491198e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9786742430161162e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786588460666383e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786427755086857e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786260250607125e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9786085882471444e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785904583937290e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785716286227128e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785520918478377e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9785318407691501e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9785108678676164e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784891653995341e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784667253907349e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784435396305667e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9784195996656493e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783948967933919e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783694220552642e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9783431662298100e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9783161198253926e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782882730726610e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782596159167249e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9782301380090251e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781998286988882e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781686770247489e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9781366717050284e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9781038011286512e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780700533451852e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9780354160545890e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779998765965463e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779634219393711e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9779260386684621e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778877129742869e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9778484306398723e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9778081770277789e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777669370665358e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9777246952365074e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776814355551679e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9776371415617527e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775917963012566e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9775453823077480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9774978815869631e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9774492755981456e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773995452350930e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9773486708063706e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772966320146480e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9772434079351160e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771889769929337e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9771333169396555e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9770764048285854e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9770182169889994e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9769587289991772e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768979156581769e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9768357509562859e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767722080440737e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9767072591999700e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9766408757962849e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9765730282635838e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9765036860533232e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9764328175986476e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9763603902732408e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9762863703481186e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9762107229462411e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9761334119948152e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9760544001751492e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9759736488699104e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9758911181076289e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9758067665042761e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9757205512017373e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9756324278029834e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9755423503037322e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9754502710203752e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9753561405139293e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9752599075097530e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9751615188127510e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9750609192177645e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9749580514148264e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9748528558889326e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9747452708139542e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9746352319402850e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9745226724757882e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9744075229595670e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9742897111280495e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9741691617728327e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9740457965896855e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9739195340180595e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9737902890704016e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9736579731504993e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9735224938600259e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9733837547923746e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9732416553127951e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9730960903237501e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9729469500143169e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9727941195923467e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9726374789979729e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9724769025969313e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9723122588520010e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9721434099707162e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9719702115273138e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9717925120566807e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9716101526178386e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9714229663242525e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9712307778379689e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9710334028242733e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9708306473632086e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9706223073138968e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9704081676271668e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9701880016014894e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9699615700766610e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9697286205590413e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9694888862714329e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9692420851198797e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9689879185687376e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9687260704143247e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9684562054462619e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9681779679842567e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9678909802765244e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9675948407442543e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9672891220544854e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9669733690013941e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9666470961732801e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9663097853793938e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9659608828071046e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9655997958756795e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9652258897480108e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9648384834558754e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9644368455875651e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9640201894788057e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9635876678385534e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9631383667302269e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9626712988158604e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9621853957551046e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9616794996324382e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9611523532636993e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9606025892062892e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9600287172650914e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9594291102469713e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9588019876690200e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9581453970673523e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9574571924815539e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9567350096012964e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9559762369516694e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9551779823564949e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9543370337465338e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9534498131617767e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9525123225202461e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9515200793715278e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9504680403966768e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9493505098231604e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9481610291471654e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9468922435304656e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9455357388730686e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9440818417248817e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9425193717007546e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9408353326276372e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9390145238720378e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9370390465571714e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9348876697457577e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9325350076814744e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9299504385456507e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9270966641709417e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9239277625992363e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.9203865108271144e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9164006353256985e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9118774501741596e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9066960058621081e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.9006952777506155e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8936558322908981e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8852703103650386e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8750938025635511e-1 * (type::diameter + 1)),
                static_cast<uniform_type>(9.8624559422953583e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8462948295338087e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.8248166290312643e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7947190356283909e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.7491371519761030e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.6708578631726145e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.4992447916055538e-1 * (type::diameter + 1)),   static_cast<uniform_type>(9.4024385932190320e-1 * (type::diameter + 1))
            };

            probability::dist_normal m_distribution = probability::dist_normal::standard;

            result_type pdf(result_type x) const
            {
                return this->m_distribution.pdf(x);
            }
            
        public:
            result_type sample_from_box_horizontal(uniform_type box_index, uniform_type uniform_random, bool& is_interior) const
            {
                result_type z = uniform_random * this->m_width_scaled[box_index];
                is_interior = (uniform_random < this->m_coverage_scaled[box_index]);
                return z;
            }

            bool is_inside_box_vertical(uniform_type box_index, result_type horizontal, uniform_type uniform_random) const
            {
                result_type f = this->pdf(horizontal);
                return (this->m_bottom[box_index] + uniform_random * this->m_height_scaled[box_index] < f);
            }

            bool is_tail_box(uniform_type box_index) const
            {
                switch (box_index)
                {
                case 0: return true;
                case n_boxes - 1: return true;
                default: return false;
                }
            }

            template <typename t_engine_type>
            result_type sample_tail(uniform_type box_index, t_engine_type& uniform_generator)
            {
                const auto r = right_tail_x;
                const auto r_squared = r * r;
                result_type result = 0.0;
                result_type u1, u2;
                for (;;) // while (true)
                {
                    u1 = (uniform_generator() - t_engine_type::min()) / static_cast<result_type>(type::diameter + 1);
                    u2 = (uniform_generator() - t_engine_type::min()) / static_cast<result_type>(type::diameter + 1);
                    result = std::sqrt(r_squared - 2 * std::log(1.0 - u1));
                    if (u2 * result < r) return box_index == 0 ? result : -result;
                }
            }
        };

        template <std::uint_fast32_t t_n_boxes, typename t_engine_type, typename t_uniform_type = typename t_engine_type::result_type>
        struct ziggurat_normal_from_engine
        {
            typedef ziggurat_normal<t_n_boxes, t_uniform_type, std::size_t, t_engine_type::max() - t_engine_type::min()> type;
        };
    }
}

#endif // AFTERMATH_RANDOM_ZIGGURAT_NORMAL_HPP_INCLUDED
